{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bayesian Estimation Supersedes the T-Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running on PyMC3 v3.3\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import pymc3 as pm\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('seaborn-darkgrid')\n",
    "print('Running on PyMC3 v{}'.format(pm.__version__))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This model replicates the example used in:\n",
    "Kruschke, John. (2012) **Bayesian estimation supersedes the t-test**. *Journal of Experimental Psychology*: General."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Problem\n",
    "\n",
    "Several statistical inference procedures involve the comparison of two groups. We may be interested in whether one group is larger than another, or simply different from the other. We require a statistical model for this because true differences are usually accompanied by measurement or stochastic noise that prevent us from drawing conclusions simply from differences calculated from the observed data. \n",
    "\n",
    "The *de facto* standard for statistically comparing two (or more) samples is to use a statistical test. This involves expressing a null hypothesis, which typically claims that there is no difference between the groups, and using a chosen test statistic to determine whether the distribution of the observed data is plausible under the hypothesis. This rejection occurs when the calculated test statistic is higher than some pre-specified threshold value.\n",
    "\n",
    "Unfortunately, it is not easy to conduct hypothesis tests correctly, and their results are very easy to misinterpret. Setting up a statistical test involves several subjective choices (*e.g.* statistical test to use, null hypothesis to test, significance level) by the user that are rarely justified based on the problem or decision at hand, but rather, are usually based on traditional choices that are entirely arbitrary (Johnson 1999). The evidence that it provides to the user is indirect, incomplete, and typically overstates the evidence against the null hypothesis (Goodman 1999). \n",
    "\n",
    "A more informative and effective approach for comparing groups is one based on **estimation** rather than **testing**, and is driven by Bayesian probability rather than frequentist. That is, rather than testing whether two groups are different, we instead pursue an estimate of how different they are, which is fundamentally more informative. Moreover, we include an estimate of uncertainty associated with that difference which includes uncertainty due to our lack of knowledge of the model parameters (epistemic uncertainty) and uncertainty due to the inherent stochasticity of the system (aleatory uncertainty)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Drug trial evaluation\n",
    "\n",
    "To illustrate how this Bayesian estimation approach works in practice, we will use a fictitious example from Kruschke (2012) concerning the evaluation of a clinical trial for drug evaluation. The trial aims to evaluate the efficacy of a \"smart drug\" that is supposed to increase intelligence by comparing IQ scores of individuals in a treatment arm (those receiving the drug) to those in a control arm (those recieving a placebo). There are 47 individuals and 42 individuals in the treatment and control arms, respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXYAAAEJCAYAAACAKgxxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nYJj/A9HTzJ6+APkqAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f12ddfbffd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "drug = (101,100,102,104,102,97,105,105,98,101,100,123,105,103,100,95,102,106,\n",
    "        109,102,82,102,100,102,102,101,102,102,103,103,97,97,103,101,97,104,\n",
    "        96,103,124,101,101,100,101,101,104,100,101)\n",
    "placebo = (99,101,100,101,102,100,97,101,104,101,102,102,100,105,88,101,100,\n",
    "           104,100,100,100,101,102,103,97,101,101,100,101,99,101,100,100,\n",
    "           101,100,99,101,100,102,99,100,99)\n",
    "\n",
    "y1 = np.array(drug)\n",
    "y2 = np.array(placebo)\n",
    "y = pd.DataFrame(dict(value=np.r_[y1, y2], group=np.r_[['drug']*len(drug), ['placebo']*len(placebo)]))\n",
    "\n",
    "y.hist('value', by='group');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first step in a Bayesian approach to inference is to specify the full probability model that corresponds to the problem. For this example, Kruschke chooses a Student-t distribution to describe the distributions of the scores in each group. This choice adds robustness to the analysis, as a T distribution is less sensitive to outlier observations, relative to a normal distribution. The three-parameter Student-t distribution allows for the specification of a mean $\\mu$, a precision (inverse-variance) $\\lambda$ and a degrees-of-freedom parameter $\\nu$:\n",
    "\n",
    "$$f(x|\\mu,\\lambda,\\nu) = \\frac{\\Gamma(\\frac{\\nu + 1}{2})}{\\Gamma(\\frac{\\nu}{2})} \\left(\\frac{\\lambda}{\\pi\\nu}\\right)^{\\frac{1}{2}} \\left[1+\\frac{\\lambda(x-\\mu)^2}{\\nu}\\right]^{-\\frac{\\nu+1}{2}}$$\n",
    "           \n",
    "the degrees-of-freedom parameter essentially specifies the \"normality\" of the data, since larger values of $\\nu$ make the distribution converge to a normal distribution, while small values (close to zero) result in heavier tails.\n",
    "\n",
    "Thus, the likelihood functions of our model are specified as follows:\n",
    "\n",
    "$$y^{(treat)}_i \\sim T(\\nu, \\mu_1, \\sigma_1)$$\n",
    "\n",
    "$$y^{(placebo)}_i \\sim T(\\nu, \\mu_2, \\sigma_2)$$\n",
    "\n",
    "As a simplifying assumption, we will assume that the degree of normality $\\nu$ is the same for both groups. We will, of course, have separate parameters for the means $\\mu_k, k=1,2$ and standard deviations $\\sigma_k$.\n",
    "\n",
    "Since the means are real-valued, we will apply normal priors on them, and arbitrarily set the hyperparameters to the pooled empirical mean of the data and twice the pooled empirical standard deviation, which applies very diffuse information to these quantities (and importantly, does not favor one or the other *a priori*).\n",
    "\n",
    "$$\\mu_k \\sim N(\\bar{x}, 2s)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "μ_m = y.value.mean()\n",
    "μ_s = y.value.std() * 2\n",
    "\n",
    "with pm.Model() as model:\n",
    "    group1_mean = pm.Normal('group1_mean', μ_m, sd=μ_s)\n",
    "    group2_mean = pm.Normal('group2_mean', μ_m, sd=μ_s)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The group standard deviations will be given a uniform prior over a plausible range of values for the variability of the outcome variable, IQ.\n",
    "\n",
    "In Kruschke's original model, he uses a very wide uniform prior for the group standard deviations, from the pooled empirical standard deviation divided by 1000 to the pooled standard deviation multiplied by 1000. This is a poor choice of prior, because very basic prior knowledge about measures of human coginition dictate that the variation cannot ever be as high as this upper bound. IQ is a standardized measure, and hence this constrains how variable a given population's IQ values can be. When you place such a wide uniform prior on these values, you are essentially giving a lot of prior weight on inadmissable values. In this example, there is little practical difference, but in general it is best to apply as much prior information that you have available to the parameterization of prior distributions. \n",
    "\n",
    "We will instead set the group standard deviations to have a $\\text{Uniform}(1,10)$ prior:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "σ_low = 1\n",
    "σ_high = 10\n",
    "\n",
    "with model:\n",
    "    group1_std = pm.Uniform('group1_std', lower=σ_low, upper=σ_high)\n",
    "    group2_std = pm.Uniform('group2_std', lower=σ_low, upper=σ_high)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We follow Kruschke by making the prior for $\\nu$ exponentially distributed with a mean of 30; this allocates high prior probability over the regions of the parameter that describe the range from normal to heavy-tailed data under the Student-T distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXkAAAD1CAYAAAC1BoUqAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f13140b7eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with model:\n",
    "    ν = pm.Exponential('ν_minus_one', 1/29.) + 1\n",
    "\n",
    "pm.kdeplot(np.random.exponential(30, size=10000), shade=0.5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since PyMC3 parameterizes the Student-T in terms of precision, rather than standard deviation, we must transform the standard deviations before specifying our likelihoods."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with model:\n",
    "    λ1 = group1_std**-2\n",
    "    λ2 = group2_std**-2\n",
    "\n",
    "    group1 = pm.StudentT('drug', nu=ν, mu=group1_mean, lam=λ1, observed=y1)\n",
    "    group2 = pm.StudentT('placebo', nu=ν, mu=group2_mean, lam=λ2, observed=y2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Having fully specified our probabilistic model, we can turn our attention to calculating the comparisons of interest in order to evaluate the effect of the drug. To this end, we can specify deterministic nodes in our model for the difference between the group means and the difference between the group standard deviations. Wrapping them in named `Deterministic` objects signals to PyMC that we wish to record the sampled values as part of the output.\n",
    "\n",
    "As a joint measure of the groups, we will also estimate the \"effect size\", which is the difference in means scaled by the pooled estimates of standard deviation. This quantity can be harder to interpret, since it is no longer in the same units as our data, but the quantity is a function of all four estimated parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with model:\n",
    "    diff_of_means = pm.Deterministic('difference of means', group1_mean - group2_mean)\n",
    "    diff_of_stds = pm.Deterministic('difference of stds', group1_std - group2_std)\n",
    "    effect_size = pm.Deterministic('effect size', \n",
    "                                   diff_of_means / np.sqrt((group1_std**2 + group2_std**2) / 2))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we can fit the model and evaluate its output."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [ν_minus_one_log__, group2_std_interval__, group1_std_interval__, group2_mean, group1_mean]\n",
      "100%|██████████| 2500/2500 [00:03<00:00, 727.76it/s]\n"
     ]
    }
   ],
   "source": [
    "with model:\n",
    "    trace = pm.sample(2000, cores=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can plot the stochastic parameters of the model. PyMC's `plot_posterior` function replicates the informative histograms portrayed in Kruschke (2012). These summarize the posterior distributions of the parameters, and present a 95% credible interval and the posterior mean. The plots below are constructed with the final 1000 samples from each of the 2 chains, pooled together."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA1cAAAIUCAYAAAD2edaGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4yLCBo\ndHRwOi8vbWF0cGxvdGxpYi5vcmcvNQv5yAAAIABJREFUeJzs3XlcVPX+x/H3LKACBgioua+5Zy65\nYJpLZtstLVMzKc2r5pJl9jNSc7muuVQaWVaaprfUTMvKNisrr+m1JE3LFc0tEJVVFhmY3x9eJwlU\nGM4AM/N6Ph4+HnA458znM8czn/mc853vmOx2u10AAAAAgCIxl3QAAAAAAOAJaK4AAAAAwAA0VwAA\nAABgAJorAAAAADAAzRUAAAAAGIDmCgAAAAAMQHMFFEFSUpIGDx6s0aNHl3QoAABc1caNG9W7d2/1\n6dNHL730UkmHA3gkmiugCCZPnqzWrVuXdBgAAFxVenq65s2bp2XLlmn16tXaunWrDh06VNJhAR7H\nWtIBAK6SkpKi0aNHKyMjQz169NA777wjq9WqTp06KSQkRL169dL48eOVlZUlk8mkGTNmyGQyafTo\n0Vq3bp0k6f7779fChQsVFRUlPz8/xcTEKCEhQbNmzVLjxo01ffp07d27V7///vs147ntttvUp08f\nff7556pZs6aaNGni+Hn+/PmKi4vTxIkTdeHCBVksFk2fPl1VqlTR0qVL9cUXXygnJ0e33nqrRo0a\npVdeeUUpKSk6cuSIjh07pvHjx+vWW2919VMKAHCR4qhZGzZsUEBAgCQpKChIiYmJV4yHmgU4hztX\n8Fgffvih6tatq/fee08+Pj6SJJvNpk6dOmn48OFasGCBevfurRUrVqh///6Kioq66v5sNpuWLVum\nJ598Uq+++qokOYpUQeTk5Khx48b64IMPtHPnTlWtWlVr167Vzz//rOTkZC1YsECDBg3S8uXL9eij\nj2rRokWObd99912tWbNG69atU2pqqiQpNjZWb775piZMmKDVq1cX9ukBAJQixVmzDhw4oJMnT6p5\n8+ZX3J6aBTiH5goe6/Dhw2rVqpUkqWvXro7lN954oyRpz549atOmjSSpdevW+u233666v/DwcEnS\nTTfdpCNHjjgV04033iiTyaSQkBA1btxYklShQgWlpKQoOjpar7zyiiIiIrR48WLHFcWyZctqwIAB\neuSRR5SQkOBY3rJlS0lS5cqVlZKS4lQ8AIDSobhq1tGjRzV27FjNnz/f0cRdCTULKDyGBcJj2e12\nmUwmSZLZ/Nd1hEvFxGQyyW63S7p4hc5sNjvWv8Rmszl+zsnJcfz89/UKymKx5Puz3W6Xj4+PFixY\noIoVKzqWnzx5UsuWLdP69evl7++ve+65x/E3q5XTFwA8RXHUrNjYWI0cOVJz5sxRo0aNrhkTNQso\nPO5cwWPVqFFDe/bskSR9//33ef7erFkzbd++XZK0Y8cONW3aVAEBATp79qzsdrvi4+N1/Phxx/o7\nd+6UJEVHR6tu3bqGx9u8eXNt2rRJkvTjjz/q448/VkJCgipUqCB/f3/t3btXJ0+eVFZWluGPDQAo\nWcVRsyZMmKApU6aoSZMmRY6XmgXkj8sI8Fi9evXSiBEjFBERofDwcFksFmVnZzv+Pnr0aE2YMEFr\n1qyRj4+PZs6cqcDAQIWHh+uBBx5Qw4YNc13Zy8jI0LBhwxQbG6s5c+YoOztbAwcOVHJysuLi4hQR\nEaERI0aoffv2TsU7atQojR8/Xp9++qlMJpNmzZqlKlWqyN/fX/369VOrVq3Ur18/TZ061TF0BADg\nGVxds44cOaKffvpJCxcudKwzcOBAdevWzal4qVlA/kz2S/eYAQ9z8uRJxcTEqGPHjoqOjlZUVJSW\nLFni1L4iIyPVo0cPdenSxeAoAQCgZgGegjtX8Fjly5fXsmXLHLMkTZgwweWPuXv3bs2dOzfP8jvv\nvFP9+/d3+eMDANwTNQvwDNy5AgAAAAADMKEFAAAAABiA5goAAAAADOD0Z67i4/P/AriAgDJKTc10\nOiB35q25e2veErmTu/cpSu5hYeUNjqbgrlSz/s5dj627xi25b+zuGrfkvrG7a9yS+8burnFLRY/d\n2Zpl+J0rq9Vy7ZU8lLfm7q15S+Turcjdc7lrfu4at+S+sbtr3JL7xu6ucUvuG7u7xi2VXOwMCwQA\nAAAAA9BcAQAAAIABaK4AAAAAwAA0VwAAAABgAJorAAAAADCA01OxA8hfYLC/fK0Fv25xwZajpITz\nLowIAFBaUCMAz0ZzBRjM12rW7OgzBV4/skWoC6MBAJQmrq4RBW3eLn2HT1aOXT5mU4H3T7MHXB3N\nFQAAgIdwpnnjgiBgHKebq4CAMvl+OZfFYlZQkF+RgnJX3pq7t+YtGZe7Oz5/HHdyB+B6thy74y4T\ngNLP6eYqNTUz3+VBQX5KTExzOiB35q25e2veUv65O1ME3fH547iTe2HxBhEoPKvZxJ0lwI0wWyAA\nAAAAGIDmCgAAAAAMQHMFAAAAAAaguQIAAAAAA9BcAQAAAIABaK4AAAAAwAB8iTBQwgr7HSZZOXb5\nmE0FXv+CLUdJCeedCQ0AcA2Bwf7ytXKtGsBFNFfANVyrcBb1u3uc+Q4TvvMEAEoHX6uZ12QADjRX\nwDUUpnAe2faN/vvGLN0+dbGCq9eRJJ36dYd+XrVYJrNZ1W5qr5seGCRJSjgeo6/nPqtqwwZLTe7I\ns6+PIgfKt1yA4/dOT0yWf4UwSZLtQqbWPzNAN90/UPU7361tb7+o0wf3yKeMnySp6T/6q3rL8CLl\nDQAonY5s+0ZbXpupe6a/kafWRJcvI1P91o5as335AsUf2ivJpLYDn1JY3Ua59tWzZ08lqKzj96vV\nmtQzcRo48Bmlp2fKYrFq0qR/KSSEZhG4HM0VYJDY36J18pdtatCgQa7l25a9rNufe1H+FcL06eTh\nqtW2s/xDK2vb2y/q+qatr7rPOydH5bt817plKhtwneP3rIx0dRgaqZBaNxQ9EQBAqXWp1gTXqJtr\n+aVa869ujdTp3gdVq21nZSQnKjn2hO6Z9oYSTxzRD6/N1D9mvJlnnwWtNTvXvKFRffro5ps76oMP\n1mj16n9rxIgnjU0QcHM0V/A4Gzd+rF9+2anExEQdORKjoUOHa9OmL3T06BFNmjRd+/f/rq+++kwm\nk1kdO3bWQw8N0OnTcZo2bZIkyWazaeLEqapatZr69u2pHj1u1yc/bJevX3l1f3audn+0Qqd278j1\nmO0Hj1VI7RtUuXEL7X1xjGN5StxJlQm4TgGhlSRJ1VuG69Sen9Swey91j5yvXz9aecU8stLT8l1+\n+PBhJZ48qmotwq+5LgDANT78cL22bt2m9PRU7di7X636DlXM1q+UeOKobh01WWeO7FfMli9lMplU\n4+ZOanrPQzp/9rQiIsboWGqWcrKz1XH4BF1XuZrWPtlHNVp30ukDu/PUmr3lfXQsJUtS7lrz2dRR\njlgurzVms9lRazKSE1Xz5o6SpKBqtXXhfIoupJ2Xr5+/Y9vz5/P/TG7iyT/y1Jr2jz2jHm2q6Ny5\nNAUFBevAgX2ueGoBt0ZzBY90/PgxLVr0lj7++EOtXLlMS5f+W5999rFWrFiq8+fPa9GiJZKk4cMH\nq0uX25SQcFaDBg1Ry5at9cknH2nduvf1xBNjdOrUSd13332y3z5Yn0wconPHDql5r0fVvNejBYoj\nLfGcyl4X5Pi9XGAFpcSdlNlildly9dMvMzVZ370yRanxsarcpKVa9hkik8mkF154QW0intCh7z5z\nrGvLTNcvH7ytC6kp8gsJU7uBY1TmsquNAADjHT9+TO+/v1qPzX9buz9aoXtnv61Dmzdq14fvKCv9\nvO6a+pok6dNJj6tWuy5KT0rQyJEjtblMPR349hPt+2q92kQ8oZTTp1Sv0x1qEzEqT60pyOdsr1Rr\nMlKSFFKn4WXLg5WeeDZXc5WYmJhvrdmx8hW1G/R0rlrjU7acLBaLsrOztX79+xo48J9GPZWAx6C5\ngkdq2LCxTCaTQkJCVbdufVksFgUHh+jw4UOy2Wx64olhkqS0tPOKjT2l66+vopdfnqclSxYrJSVZ\nDRpcHJPu7++vhg0bStFn5FehorLSCjvrnj3v76aCzfTXqu8w1bnldll9y2jTvGf1x383y5aZoZY3\n3aTkilVyrdug230KqlZbgVVqaNf65Yp+/y21G/R0IWMFABTGpVrjFxSi4Bp1ZTZbVC6wghKOHVZO\ntk2f/+sJSVJWRppS42MVEHa9VqxYpF9PxCvzfIpCa18cRu5bzl8VataTJINrjT3vWn+rQWPGjNGh\nmh3y1Jqw+k1V/m+1RpKys7M1bdoktWzZWq1btylknIDno7mCR7JYLPn+nJycpG7dbte4cRNyrT9z\n5lS1bdtOPXv21rffbtLWrVvybCtJdrtdu9Yvz3dYYFC12nni8AsOU3riWcfv58+dUbmgkALl0PD2\nXo6fq7fsoIRjh5V48g8lpJ5W3Kdf6fy5eFmsPvIPqaiabW51rFvz5k7aumRegR4DAOC8y2uE2fzX\nz5mpyaodfps6DBmXa/0fXpuhAV1uUfWG3XV027c6vvM/kiTTVWrN34cFFqbWmC3WXMvTEs7IL6hC\nrm379+/vuDN2ea1JPX1KJ3b+J1etqdLsZj333HOqXr2GHntsaKGeK8Bb0FzBqzRo0Eg7d/6sjIwM\nlSlTRgsWzNfw4aOUmJioqlWryW63a8uW75SdnXPFfRRmWGD5itcrK/28Uk7/Kf+QMJ3Y+R91GjX5\nmttlJCfq+0XTdNszL8hstSr2t2jVatdFLR78p2OISPT7SxQQVllVmt2sTXPHqd2gpxUQWll//hbt\nmD0KAFD8Quo0UOzenbJlZsjiW0bbly9Q6/7DlZmSpBo1auio3a5jP/0ge861a01BhgVeXmtstiBH\nrclISdIva99Sw9t66uyRA/ILDpVPub+GBGYkJ2rIkOdUe+i0PLXmkstrzeEtX6iij48GDx5W9CcJ\n8FA0V/AqlSpVVufO3TRy5BCZzWZ16tRZZcqU1X333a+XX56nSpWuV+/efTVnzgz997/bCrXvA998\nrMM/fKHzJw4p5rUZCqxaS51GPq/2g/9P371ysaGq1b6bAqvU0JmYfdqxIkqp8X/qnZ/KKNPvE3Ud\nO1PHfvpBvn4BqtnmVl3fpKU+mTRUFquvKtSqr1ptOl/xsRvd/oC+fXGCrGXKyVq2rG55fMIV1wUA\nuFZASCXVattFG6eOkMlkUc2bO8rqW0YNut2n6dOnK7N8mBr16K2tb76gk7u2F2rfl2rNuT8Oaks+\ntebhpT6OWhMoKaR2Q33y/DCZzGa1f+zicPGDmz911Jq2bdtqaQFrze9frNMZnxyNGnXxrlWtWnX0\nzDORzj5NgEcy2e32vw/ULZD4+JR8lwcF+Skx0TtnLvPW3D0977Cw8i7/kl9Xr3+l87UoPP24Xw25\nO5d7Ub9wuyjS0y/IarVccz2LxXzVO9ellbvGLblv7Jfi9vGxlLrXfFevn5WVXeD1jeSu/1ck943d\nXeOWih67j8+1a0Z+uHMFAPB4qamZBVrPXRtnd41bct/YL8VdkhcNSkpJHS93/b8iuW/s7hq3VPTY\nnT23aa7gdQKD/eVrNZd0GAAAAPAwNFfwOr5Wc6GHQAAAAADXwuV7AAAAADAAzRUAAAAAGIDmCgAA\nAAAMQHMFAAAAAAZgQgsAAID/KcyMst44DTuAq6O5AgAA+B9mlL06W469UE3lBVuOkhLOuzAioHSh\nuYLb43urAAAoHlazieYTuAqaK7g9rjJeHVcZAQAAigfNFeDhuMoIAABQPJxurgICyshqteRZbrGY\nFRTkV6Sg3JW35u6teXuyghxPbz7u5O6duQMAcC1ON1epqZn5Lg8K8lNiYprTAbkzb829pPNmtibj\nFeR4lvRxL0nk7lzunKuA92FoOrwNwwIBAADgEgxNh7dhijUAAAAAMADNFQAAAAAYgOYKAAAAAAxA\ncwUAAAAABqC5AgAAAAAD0FwBAAAAgAForgAAAADAADRXAAAAAGAAmisAAAAAMADNFQAAAAAYgOYK\nAAAAAAxgLekAAAAAXCUw2F++Vq4lAygeNFcAAMBj+VrNmh19psDrR7YIdWE0ADwdl3IAAAAAwAA0\nVwAAAABgAJorAAAAADAAzRUAAAAAGIDmCgAAAAAMQHMFAAAAAAZgKnYAudhy7AoLK1+gdcPCyuuC\nLUdJCeddHBUAAEDpR3MFIBer2cR3wsDjBASUkdVqueZ6FotZQUF+xRCRsdw1bsm9Y4drXOn/gzv/\nX3HX2N01bqnkYqe5AgB4vNTUzAKtFxTkp8TENBdHYzx3jVtyfewFvROP0sGWY5ePz5UvhJjNuf/m\nLqMn3PUcdde4paLH7uxrB80VAAAASgVGT8DdMaEFAAAAABiA5goAAAAADEBzBQAAAAAG4DNXKHUC\ng/3la6XvBwAAgHuhuUKp42s182FWAAAAuB1uDwAAAACAAZy+c3WlL2R05y8bKypvzd1b88ZfvO34\ne/P/eW/OHQCAa3G6ubrSFzK685eNFZW35m503nzho/vxtv/33nquS0XLnXMbAODp+MwVAABwG0x6\nBKA0o7kCAABug0mPAJRmXPoBAAAAAAPQXAEAAACAARgWCKBIbDn2Qk1UcMGWo6SE8y6MCADgLahB\nKG1orgAUidVs4vMPAIASQQ1CacOwQAAAAAAwAHeu4HJMmwsAAABvQHMFl2PaXAAAAHgDbicAAAAA\ngAForgAAAADAADRXAAAAAGAAmisAAAAAMADNFQAAAAAYgNkCAQBAyTGbFRZWvqSjAABD0FwBAIAS\n42Mx8XUdADwGwwIBAAAAwAA0VwAAAABgAIYFAihWthx7oT5fccGWo6SE8y6MCADgLQpbgyTqEAqH\n5gpAsbKa+XwFAKBkFLYGSdQhFA7DAgEAAADAANy5QqEEBvvL15q3J2caXQAAAHg7misUiq/VzO10\nAAAAIB8MCwQAAAAAA9BcAQAAAIABGBYIAPB4AQFlZLVarrmexWJWUJBfMURkLHeNG3AXRT2/3PUc\ndde4pZKLneYKXs+ek6Otb81VwvEYWaw+av/P/1NQ1Zra9vaLOn1wj/aGBupYSpaa/qO/qtx4s76e\nF6nMlGS1eWS0KjVoJknaNPdZtX9srPxDKubad8rpP/XtyxN078yljmXR7y9RmfKBanxHb70/6gHt\nrllVJ9NylG27oCrNblbLPkOUcvpPfTguQqG1G8ouuyxWH7Xo809VrN+0WJ8bwFOkpmYWaL2gID8l\nJqa5OBrjuWvckndMiHR5ndkb7KeqfZ/KVWd8ylx8A5hfnVGLLpKKVmf8QyrKZLbkW2f23thMf6Rc\noM5cQ1HPL3c9R901bqnosTv72kRzBa937KcfdCEtVfdMW6zk2BPavnyBuj87V1kZ6eowNFJze4U7\nJvE4uWu7KjW4UXU79tDOVW+oUoNmOh69VRVq1stT8ArqzTff1CsH0mXPydEXM55S3L5d8qtQUYFV\naujOyVGSpOTYE/p6XqRu+78XJDFBCAC4k8vrTP+QNA0aNzlXnQmpdYNj3b/XGfXrUuQ60/25+fIp\n65dvnVmxYoVmR5/JVWfKV6pqVOqA1+EzV/B6ybEnFFavsSTpusrVlHomVjk52cpKz3u1IyMlSeUC\nK8gvKFQZKYnKycnWbxvXqNm9A4och8lsVmjdRkqOPZHnb9dVrqam/+ivXz/+d5EfBwBQvC6vMzVq\n1ChUncnOps4A7sTpO1dXGr/uzmMzi8qbc3dnwdXraO/G1Wp8Vx+lxJ5Q6ulTykxOki0zXb988LYi\n1r2mM75BajdwjPxDKurkL9uU9Ocx+YdU0sFvPlGdDt21+6MVSk84o0Y9ekt/m3o+6dQxfTZ1lOP3\n1Pg/1eSeh/LEYbuQqT/37lTdjj3yjTOkVn0d/OZjY5N3E6XtvPLmc92bcwecdXmdiYmJyVNnLqSm\nyC8kLN86s3bt2jx1JqT2Dbn2f3md2VveR4dijlFngBLidHN1pfHr7jw2s6i8IXdPHBtfrUV7xR34\nVZ9NGangGnUVWLWm7LKrQbf7FFSttmbd3VIPTZqv6PffUttHn9LBbz/RtmUv6eb+I7Tz/bfUvOcj\nSjl9Su0GPa3NCyZJ94fn2v/lw/uki2PhLzdkyBCdTMuRJDXodq+Cq9dRyuk/88SZY7PJZL72B/I9\nUWk7r7zhXL+SouTuia8fQEFcXmcyWzbJU2cCq9TQrvXL860zm754R9d17Zerztw2bk6u/V9eZyJb\nhKrv+Bdy/f2rWWMd9YM6U3i2HHuhXr8u2HKUlHDehRGhNOMzV4CkVn2HOn5eO/pBlbsuWDXb3OpY\nVvPmTtq6ZJ5MZrM6jpgoSYp+/y01+0d/pZ6JVUBoZVnLlM13iMe1XPrM1bWcidmnCrXqF3r/AICS\nd6nORLYI1acduxS4zowZPFhLdhwuUp259Jmra6HO5M9qNjk+e10QkS34bLQ34zNX8Hrn/jioLa/P\nlCSd+GWbQmo3kMls1qa545R6JlaS9Odv0QquXsexTdq5eCXHntD1TVqpXGAFnT8bJ1tmhiy+vi6J\nMTn2hPZ+ulpN7u7rkv0DAFzn8jrz/fffF6rOtGvXjjoDuBHuXHm5wGB/+Vq9u8cOrl5X9pwcffL8\nUPn6lXdcMWx0+wP69sUJinjnOp3KsuiWxyc4tvll3du6qfdgSVLlxi20d+NqffavJ9T8/kcNi+vS\nGPqcnGyZzGbdMnyCAkIrG7Z/AEDxuLzOHKpcQe0ee1bSX3XGWqacrGXLlkidiYiI0NGkDOoMYBCa\nKy/nazV7/a3uy4dgXK5q87aq2rytIluE5nmOwv85zvGz2WJV92fn5bvv8hWvz/XdI5LU4sHBjp8f\njPpA/v7+ktLzbBexbFNhU/FIjHUH4O4urzOX15RLdSY/RtaZK20XsWxTvjUOgPNorgCUaox1BwAA\n7sK7x4MBAAAAgEForgAAAADAAAwLBAAAhmGiJADejOYKAAAYhomS4O2uNBHTlSZnYiImz0JzBcCj\nMLsgAKAkMRGTd6O5AuBRKGoAAKCkMCgaAAAAAAxAcwUAAAAABmBYYBHFxBxSZORY9e3bX4MHD1Jc\nXKymTZuknJwchYSE6vnn/yVfX199+eVnWrPmPZlMJt133/265577cu1n4sRnlZiYIElKSUlW48bN\n9PjjI9W//wOqXbuuJCkoKFjTp7+gs2fPaMaMqcrMzFBwcLDGj58iPz+/Ys8dcEcJx2P09dxn1fiu\nvmp8R2/9+eefeuqpp/Ocs19//aVWrVopk8msVq1u1rBhI3PtZ8+e3Xr11QWyWq3y8fHV88//S8HB\nwbrvvh6qXr2mY70FC16TxWJRdPTPev75SD333CR16NCxuNOGG7m8rjzwQN8C1ZWHHuqnrl3vzLWf\nK2334Ycf6JNPPpKPj1V9+z6szp27yWazafbsaTp16qRsNptGjnxKzZvfVELPAOB5/l57Us/E6YdX\np8mek60/a1fRuHGTCvR+8Y8/jmrOnBkymUyqXr2Gxo6NlNVqzfe83rz5a7322isKC6soSbr55rZ6\n9NHBJZG+V6G5KoL09HS99NJctWrVxrFsyZLFuv/+Pura9TYtWrRAn366QXfccbfefvtNvfnmO/Lx\nsWrQoIfVqVNnXXddoGO76dNfcPw8c+ZU/eMf9yk9PV033niTZs2an+txV6xYpo4db1WvXr31+eef\nau3aVXrkkcckMQUucDVZGena9vaLur5pa8eylxcs0MCBj+jOO+/UnDlz9N13X6hXr156441XtWHD\nBvn7+6tPnz5KSopTvXr1dMGWI9ntWrXq35o4caqqVq2mpUvf0Mcfr1dExCCFhIQpKuqNXI978uQJ\nrV79b914I29WcXXO1pV//jNCrVuH56or+W3XuXNXrVq1UsuXr5IkPfnkcLVv30GbNn2psmXLadGi\ntxQTc1izZk3Vm2++U+z5A54ov9oT/f5batjjftVu11X6cqm+++4L9ezZU++8s0Rr166Vj4+Pevbs\nqV697lFQUJBju0mTFmnY8Md1Y9NWWrbsLX3zzSbdfHObfM/r9PR0PfBAH/Xp07/Yc/ZmNFdF4OPj\no3nzFmjlyuWOZdHRP+uZZ56TJN1yy61avfrfqlGjpho1aqKAgABJUvPmLbR79y7dckunPPs8duyo\nUlNT1bhxU8XEHMr3cU+cOKY77rhbktS2bXs9/3yko7liClzgyiw+PuoeOV+/frTSsWzHf/+r6+4f\nrV3RZxRXo7U2fbpKxxrdri7T31bUwQxJGTpr9lPUf4+qckqQIluEKisr23FBxG63Kz4+Xjfe2Fzp\n6enKycnJ87ghIaGaMWOuZs+eVlypwk05W1datmyVp67kt12DBg1Vo0YtlSlTRpJUr94N2rt3j3r0\nuEu33dZDkhQcHKykpCTHfrhoBxRNfrUn9rdohf/z/yRJ3W/rpudeXqxt2SEyV7tBrx7KlJQpn9pN\nNX7tZtVodYtju5/3x2jmTc1ls0lt2rTT+vVrVa1atXzP67Q0ZsItCTRXRWC1WmW15n4K09PT5evr\nK+niG6qzZ8/q7Nmzua46VKgQorNn82+A1qxZpd69+0qS0tLS9ccfRxUZ+bSSkhLVu3c/det2u+rU\nqacff9yihg0badu2rY7hhACuzmyxymzJe85afC6es+UCKygt4awkyaecv6SLQzlS42NVsX7TPPvb\ntm2rXn55nmrVqqUePe5SQsI5JSSc08SJ43TmzBl163a7Hnywn8qWLevizOApnK0roaGheepKfttV\nq1ZdMTGHlJiYKF9fX+3Zs1stWrTM9bhr1ryn7t3vcOyHi3ZA0eRXe2yZf9WesLAwpSWcVXriWZUt\n/9d5XS6wgtL/V5MuCa5eR998u1kP3N9Le/bsVGpqkpo3b6Q//oiRxZKlMmXKaN++Pbr11g4ym3P0\nww/fa8dP25R14eJw3/r1b3B9wl6OS1EGM5lMjp/tdrsu/mrPtc7F5Sb9XVZWln799Re1bHnxtnGl\nSpU0cOAQzZw5TzNnztPrr7+qM2fOKCJikI4ePaJRo4bq3LmzstvtefYFoGD+fi5e/nvSn8e1eeFk\n3frEZJmtea9FtWsXrvfe+0BXDURHAAAgAElEQVQ1atTSypXLVLZsWQ0Z8rgmTZquF1+M0meffax9\n+353eQ7wbM7Wlfy2u+66QI0Y8aQiI5/WjBmTVbt2nVw15IMP1mj//n0aNGiIS3IB8D95zk+T8pzX\nf1tPkm4eMEpffvG5br3/IX1/6rxiki/o9SM21X/wcd37yBD1enyMLoRU14dHkrU/uKFC73xEy95+\nW4MGDdH06ZNcnxdoroxWtmw5ZWZmSJLi408rJCRUoaFhOnv2rysPZ87EKyQk75W9X375WY0aNXH8\nHhZWUQ/2fUCVKgXqhhtqqnnzZkpKilOdOlW0aNErWr36Pd17712qXr2awsLKF+qLUwFcVK5cOdku\nZEqS0s7Fq1xQiCTp/NnT+mZ+pDqOmKiQWnmv9H333beSLr6B7dy5q3bv/kX+/gG6556e8vX1lZ+f\nn1q3bqPDhw8WXzLwSAWpK6dPx+WpK/ltJ0m9HrhPH3zwvt5443X5+lrUqFE9hYWV1+bNn2vHjq16\n663Fuv76YOoK4ELWMn/Vnri4OJULCpFfcJjSk8451kk7Fy+//9WkSwJCK2nx4sW68/lXVLF+EwWE\nVZYk1W7XVfdMW6yuT8+U3W5XQFhlhdVrrOubtJJ08SMpCQkJys7OLqYMvRfNlcFat26jzZu/kSR9\n9903ats2XE2aNNW+fb8pJSVFaWlp2r17l5o3b5Fn299//0316tV3/L59+49a+PKLmh19RtN+PK6t\nv+zVp+cDNWjeUg2c86ZmR5/RuNf+LVv9NpodfaZQwzYAXBQeHq4/tm+WJB3972ZVu6mtJGnL4llq\nP/j/FFq7Qb7bLV36hg4e3C9J+u23PapRo6YOHz6k6dMny263y2azaffuXapdu06x5AHPVZC6Eh0d\nnaeu5LedzWbT4EGPavr2k5r07X5tid6jjbbKmvD5Lr28dKVqD5mql35LcdQU6grgGlWatnbUni+/\n/FLVbmqrsPpNdObw78o8n6KsjDSd3v+rKjVqnmu76Pff0ubNF7c7uPlTVW95i3Kybfps6ijZLmQq\nLfGszh09qNA6DfXLB2/r6PaLFwJjYg4pKChIFoulONP0Snzmqgj27ftdUVEvKTb2T1mtVv3ww2ZN\nmDBVM2ZM0UcfrVPlytfrzjvvkdVq1eOPj9LTT4+SyWTSY48NUUBAgA4e3K/vv9+swYOHSZLOnj2j\nqlX/mk2sZcvW+vbbL7T9+WGy52Trxp4R8q8QphqtO+rbF8crZsuXCqxWWy37DS2ppwBwK2di9mnH\niiilxv8pk9WqP7Zv1prFC9Rv5NPav+lD+YdVVr1Odynp1DHF7dul6DVvObZtcndf+YdW0sIf3tXw\n4SP13HPPa/78F2SxWFSmTJn/TcVeQYGBgRo69FGZTGZ16NBRjRs31datW/Tuu+/o2LE/tH//71q7\ndpVeeunVEnwmUFr9va58++3Xmjx5+jXryvDhI/LUlcGDh2n69El5trvjjjsUNWmYrL5ldcvj42W2\nWHXgm4+VkZqsr2Y/44jl9gkvyWL1KcFnA/AM+dWeTk9M1pbXpmv/pg/V5oaaqtfjnzJbrWr90HB9\nOfNpmUzSTb0HydcvQGePHtCxHd+rxYP/VJ0O3RUVNUtxF0y6vnELVW8ZLkmq1a6LPv3beV234x3a\n8toMDdjykTIyMhUZ+XwJPxPegeaqCBo2bJRryuWgID8lJqbp5ZcX5Vm3S5fb1KXLbbmW1a/fQPXr\n/3VVfMyYcbn+7uPjo/nz5+e5clguMFh3TX3NiBQArxJap6HunByVa1mlSqHqMWFBrmWBVWrokXe+\nyXcfo3uFKysrWw0bNtbrry/N8/cnnng6z7Lw8FsUHn5LnuXA3/29rlxyrbpyqf5cXldCQ0Pz3e7h\nhx/W8cY9ci1r9dDjavXQ40akAOBv8qs9khy1J7JFqOO9Xq12XVSrXZdc64XUusExPD2wSk2tXbs2\nz3vDRj0eUKMeD+RaVr7i9bpzcpQiW4QqPj7FsHxwdTRXxYwpbQEAAADPRHNVzJjSFgBglMsv2DH5\nBID82HLshXp9uGDLUVIC35HlLJorACgEW45dPj4WChVKhcJesJO4aAd4G6vZxIX9YmSyO/klSVca\nu3lp3Lc3KkjuYWHlC/0f/FrrH96xRR/NGqf4o0z5DFxJWK36uu+5Oap7c+7PPhXkHCvK+pe28ZTx\n7kV5jS/JOysFff7drYYVtqZI1BWgOF2p9lzO1XXImfUvvWa622vi5Yoau7M1iw//eID1M8ZSAIFr\niD96UOtnjC3pMAC3QF0BjOGOtefSMMKwsPKOkRpX+xcY7F/SIZcqHj8ssLATSDB8B4DRGO/uvahB\nANwNwwiLxu2aK2dm2yvMf5BnmocU6k1QVo5dPmaT4/eSGPbSa8J8bZj9rE4fOVDsjw24i4q1b9C9\nkS+UyGMXtlAV9nWosG/IecPvvNJWg1yFugIYoyRrT3Fx9QVEd6tZTn/m6ko2b96szp07G7lLt+Gt\nuXtr3hK5k7v38fTc3TU/d41bct/Y3TVuyX1jd9e4JfeN3V3jlkoudsM/c/Xdd98ZvUu34a25e2ve\nErl7K3L3XO6an7vGLblv7O4at+S+sbtr3JL7xu6ucUslFzsTWgAAAACAASxTpkyZYvROa9WqZfQu\n3Ya35u6teUvk7q3I3XO5a37uGrfkvrG7a9yS+8burnFL7hu7u8YtlUzshn/mCgAAAAC8EcMCAQAA\nAMAANFcAAAAAYACaKwAAAAAwQIGaqwMHDui2227TypUrJUl//vmnIiIi1L9/fz355JO6cOGCJGnD\nhg164IEH9OCDD2rt2rV59nOl7Uozo3KfNm2a7r//fkVERCgiIkKbN28uzjScUtDck5KSNHjwYI0e\nPTrf/bjbcTcqb08+5hs3blTv3r3Vp08fvfTSS3n2427HXDIud08+7q+++qr69u2rPn36aNGiRXn2\nU9qPe05Ojp5//nn169dPEREROnz4sA4fPqyHH35YAwYM0MSJE2Wz2XJtc/78eY0aNUoRERHq16+f\nfvjhh2KN2V3rr5FxDxw4UAMGDNDAgQMVHx/vFnFf8sMPP6hBgwYujdno2LOysjR27Fj17t1bjz76\nqJKSktwi7h07duihhx5SRESEhg0b5vK4CxN7aXufZGTcxXl+Ghn7Ja44R6/ZXKWlpWnatGlq3769\nY9nChQvVv39/vfvuu6patarWrl2rtLQ0vfrqq1q2bJlWrFiht956S4mJibn2ld92pZmRuaelpWnG\njBlasWKFVqxYUeq/kK2guUvS5MmT1bp16yvuy52Ou5F5e+oxT09P17x587Rs2TKtXr1aW7du1aFD\nh3Lty52OuWRs7p563E+cOKH9+/dr9erVeu+99/Thhx8qLi4u175K+3H/+uuvlZKSolWrVmnGjBma\nM2eO5s2bp6FDh2rlypW6/vrr9dlnn+XaZv369apdu7ZWrFihBQsWaMaMGcUWr7vWXyPjfvnll9Wn\nTx+tXLlS3bt319tvv+0WcUtSZmam3njjDYWFhbksZlfEvmbNGgUHB2vt2rW666679NNPP7lF3LNm\nzXK89rZo0UKrV692WdyFiV0qXe+TjIy7OM9Po2OXXHeOXrO58vX11ZtvvqmKFSs6lm3fvl3dunWT\nJHXr1k0//vijdu3apWbNmql8+fIqW7asWrdurZ07d+baV37blWZG5n7+/Plijb2oCpq7JE2fPl0t\nW7a84r7c6bgbmbenHvNy5cppw4YNCggIkMlkUlBQUJ4i507HXDI2d0897tWqVdPChQslXbwiaDKZ\nFBAQkGtfpf24Hz16VDfeeKMkqUaNGjp16lSuZR07dtR//vOfXNsEBwc7jnFycrKCg4OLLV53rb9G\nxj158mT16NFDUu5jUdrjlqTXX39d/fv3l6+vr8tidkXs3377re69915JUt++fR37KO1xX/7/Iykp\nyeXnqru+TzIy7uI8PyVjY5dcd45es7myWq0qW7ZsrmXp6emOQMLCwhQfH68zZ86oQoUKjnVCQ0Pz\n3B7Mb7vSzMjcz58/r6ioKEVEROiZZ55x+X/Aoipo7pLyvMH6O3c67kbm7Q3H/MCBAzp58qSaN29e\noO1KKyNz9+TjLl0sWPfcc49GjBghf3//Am9XGtxwww3asmWLsrOzFRMTo+PHjys0NFTfffedpIvD\nQ86cOZNrm7vvvlunTp1S9+7dNWDAAD377LPFFq+71l8j4/bz85PFYlF2drbeffdd/eMf/3CLuI8c\nOaJ9+/bpzjvvdFm8lzMy9pMnT2rHjh0aPHiwxowZ49LXMCPjfu655zRy5Ej16NFDP//8s3r16uWy\nuAsTu1S63icZGXdxnp+SsbG78hx1akILk8nk+PnS12T9/euy7HZ7rvWutJ27cTb3fv366ZlnntGK\nFStUt25dvfLKK64P1mDOHj93P+7Oxu/px/zo0aMaO3as5s+fLx8fnwJv5y6czd3Tj/vEiRP12Wef\nacmSJTp+/HiBtysNbr31VjVr1kwPP/ywli9frjp16mjOnDn67LPP9Mgjj8hut+eJ+6OPPlKVKlX0\n1Vdfafny5Zo2bVoJRX+Ru9ZfZ+OWpOzsbI0bN07t2rXLNRyoODgb96xZs/Tcc8+5PsCrcDZ2u92u\n66+/XkuWLFH9+vW1ePFi1wd7GWfjnj59uqKiovTFF1+oVatWevfdd10f7N+46/ukojx+SZ6fkvOx\nu/Icdaq5KleunDIyMiRJcXFxqlixoipVqpTrit/p06fzjGHMbzt342zu3bt3V+3atR0/79+/v/iC\nNoizx8/dj7uz8XvyMY+NjdXIkSM1e/ZsNWrUqMDbuRNnc/fU4/7nn3/q119/lSQFBgaqZcuWjt+v\ntl1pM2bMGK1atUpTp05VcnKyKlWqpMWLF+udd95R8+bNVbVq1Vzr79y5U7fccoskqWHDhoqLi8sz\n6UVxctf662zc0sU7EjVr1tSoUaOKLd5LnIk7Li5OMTExeuaZZ9SnTx+dPn1aAwYMcIvYpYt3hS59\nVuWWW27J87lSV3M27v3796tVq1aSpPDwcO3Zs6f4gv4fd32fVJTHL8nzU3Iudlefo041V+Hh4fri\niy8kSV9++aU6duyo5s2b69dff1VycrLOnz+vnTt35vkgWX7buRtnc3/88cd16tQpSRfHh9avX7/Y\nYy8qZ4+fux93Z+P35GM+YcIETZkyRU2aNCnUdu7E2dw99bifO3dOU6ZMkc1mU3Z2tvbu3etoIq+2\nXWmyb98+x5XK77//Xo0bN1ZUVJRjRsd169apa9euubapWbOmdu3aJenicCl/f39ZrdZijfty7lp/\nnY17w4YN8vHxueaMX67iTNyVKlXSpk2btGbNGq1Zs0YVK1Z0zGxW2mOXpE6dOjlmxczvPC+tcYeG\nhjoawV9//VU1a9Ys1rivFLsrtzOKs49f0uen5Fzsrj5HTfZr3EPbs2ePXnjhBZ08eVJWq1WVKlXS\nvHnzFBkZqczMTFWpUkWzZs2Sj4+PPv/8cy1ZskQmk0kDBgzQvffeq99//11fffWVRo8erdOnT+vZ\nZ5/Ns11pZWTuW7Zs0UsvvSQ/Pz+VK1dOs2bNUkhISEmneEUFzd1sNmvgwIFKTk5WXFyc6tevrxEj\nRigoKMgtj7uReXvqMT9x4oR69uzpmARAkgYOHOgYOuVux1wyNndPPe4+Pj5avHixNm3aJLvdrs6d\nO2vUqFFu9Rqfk5Oj8ePH68iRIypfvrxeeOEFJSUlady4cfLx8VHbtm311FNPSbp4h2vWrFnKzs7W\n+PHjdfbsWdlsNj355JPFNvTFXeuvkXH369dPmZmZjs9P1K1bV1OmTCn1cV+ua9eu+uabb1wSsyti\nT09P14QJExQfHy9fX1+98MILCg0NLfVx79y5U3PmzJGPj48CAwM1c+ZMXXfddS6JuzCxl7b3SUbG\nXZznp9GxX87oc/SazRUAAAAA4NqcGhYIAAAAAMiN5goAAAAADEBzBQAAAAAGoLkCAAAAAAPQXAEA\nAACAAWiuAAAAAMAANFcAAAAAYACaKwAAAAAwAM0VAAAAABiA5goAAAAADEBzBQAAAAAGoLkCAAAA\nAAPQXAEGS0pK0uDBgzV69Gintt+xY4fOnj2bZ/no0aO1ffv2ooYHAEAuGzduVO/evdWnTx+99NJL\nhd6eugX8heYKMNjkyZPVunVrp7f/4IMP8i1SAAAYLT09XfPmzdOyZcu0evVqbd26VYcOHSrUPqhb\nwF+sJR0AUJxSUlI0evRoZWRkqEePHnrnnXdktVrVqVMnhYSEqFevXho/fryysrJkMpk0Y8YMmUwm\njR49WuvWrZMk3X///Vq4cKGioqLk5+enmJgYJSQkaNasWWrcuLGmT5+uvXv36vfff79mPG+88Ya+\n+uormc1mdenSRc2aNdOmTZt08OBBvfLKK/r000+1ceNG1apVS4mJia5+egAApUxx1K0NGzYoICBA\nkhQUFHTVekPdAq6OO1fwKh9++KHq1q2r9957Tz4+PpIkm82mTp06afjw4VqwYIF69+6tFStWqH//\n/oqKirrq/mw2m5YtW6Ynn3xSr776qiQ5ClRBLF26VO+9955WrVql6667Th06dFCjRo00a9YsBQQE\nOP42bdo0HTx40PnEAQBuqTjr1oEDB3Ty5Ek1b978ittTt4Cro7mCVzl8+LBatWolSeratatj+Y03\n3ihJ2rNnj9q0aSNJat26tX777ber7i88PFySdNNNN+nIkSOFjqdHjx4aNGiQ1qxZo3vvvTfX3/74\n4w/Vq1dPZcqUUUBAgJo0aVLo/QMA3Ftx1a2jR49q7Nixmj9/vqOJyw91C7g6mit4FbvdLpPJJEky\nm//673+pkJhMJtntdklSTk6OzGazY/1LbDab4+ecnBzHz39fryCmTp2qKVOmKD4+XgMGDMi1b7vd\nnivGS3EBALxHcdSt2NhYjRw5UrNnz1ajRo2uGg91C7g6mit4lRo1amjPnj2SpO+//z7P35s1a+aY\n2WjHjh1q2rSpAgICdPbsWdntdsXHx+v48eOO9Xfu3ClJio6OVt26dQsVS2pqqqKiolS3bl2NGjVK\nQUFBSk1Nlclk0oULF1SjRg0dPnxYWVlZSk1NdcQNAPAexVG3JkyYoClTplzzThN1C7g2JrSAV+nV\nq5dGjBihiIgIhYeHy2KxKDs72/H30aNHa8KECVqzZo18fHw0c+ZMBQYGKjw8XA888IAaNmyY66pe\nRkaGhg0bptjYWM2ZM0fZ2dkaOHCgkpOTFRcXp4iICI0YMULt27fPE0tAQIASEhLUu3dv+fn5qUWL\nFgoKClKbNm00ZswYLVq0SD179lTfvn1VrVo1NWvWrFieIwBA6eHqunXkyBH99NNPWrhwoWOdgQMH\nqlu3bnlioW4B12ayc88WXuTkyZOKiYlRx44dFR0draioKC1ZssSpfUVGRqpHjx7q0qWLwVECAHAR\ndQtwL9y5glcpX768li1b5pghacKECS5/zN27d2vu3Ll5lt95553q37+/yx8fAOC+qFuAe+HOFQAA\nAAAYgAktAAAAAMAANFcAAAAAYACnP3MVH59iZBwlJiCgjFJTM0s6DEOQS+njKXlI5FJauVMuYWHl\nS+yxjapZ7vR8FwZ5uRfyci+empfkubkFBJRRuXK+Tm3r9XeurFZLSYdgGHIpfTwlD4lcSitPysUd\neOrzTV7uhbzci6fmJXlubkXJy+ubKwAAAAAwgtPDAgMCynhEt2qxmBUU5FfSYRiCXEofT8lDIpfS\nypNyAQDA3TndXHnK+MqgID8lJqaVdBiGIJfSx1PykMiltHKnXEryM1cAABQHhgUCAAAAgAGcvnOF\n0ikw2F++1oL3zBdsOUpKOO/CiADA8/HaCwCQaK48jq/VrNnRZwq8fmSLUBdGAwDeobCvvc80DynU\nMEmaMQBwDzRXAACPZ9QkTEZNIGI1mwp9IcyVE5d46sQo5OVeyMv9eGpuFovzn5yiuQIAeDyjJmG6\n0gQixTFZhysnLnGniVEKg7zcC3m5H0/NLSjIT2azcxfkmNACAAAAAAxAcwUAAAAABqC5AgAAAAAD\n0FwBAAAAgAForgAAAADAADRXAAAAAGAAmisAAAAAMADNFQAAAAAYgOYKAAAAAAxAcwUAAAAABrCW\ndAAoPc6fT9W0aZOUmpqqnJwcjRs3QbVq1c61TlxcrMaP/z+1aNFKo0Y9JUk6duwPzZ07U5Jkt9v1\n7LMTVb16DcXFxWrKlAmy2bJ0ww0N9X//N77YcwIAFNw332zSrFlTtXjx26pTp16ev+dXA86ePaMZ\nM6YqMzNDwcHBGj9+ivz8/LRz5096/fUoWSxmVa9eU5GRz8ts5pouAM/GqxwcVq36t5o1a66oqDc0\nYMBALVmyOM86s2b9S61a3Zxr2YcfrtXgwcP0yiuLdffd9+rdd1dIkqKiXla/fgP05pvvyGy2KDY2\ntljyAAAUXnT0z9q27T+qW7f+FdfJrwasWLFMHTveqldffVO33HKr1q5dJUmaM2eGpk9/Qa+9tlRp\naWnavn2rS+MHgNKAO1el0MaNH+uXX3YqMTFRR47EaOjQ4dq06QsdPXpEkyZN1/79v+urrz6TyWRW\nx46d9dBDA3T6dJzGjJkqk0k6mpShjsMn6LrK1bT2yT6q0bqTTh/YLV+/8ur+7Fzt/miFTu3eIUna\nW95HFy7YNHZspAYMGOi4qhgUFKTk5KQ8sc2cOVebN3+jmJjDjmWjR491/BwXF6uKFSsqJydHu3dH\na8qUGZKksWOfdeVTBgAe4+DmTxX7+y/KTElSwokjatV3qB5f/J0OHDh41RowbdokSZLNZtPEiVNV\ntWo19e3bUx07dtavv+5SQEB5zZ37slaseFs7dmzP9ZhTp05RgwYN/3dHaugVY8uvBpw4cUx33HG3\nJKlt2/Z6/vlIPfLIY1qyZIX8/QMkSUFBwUpKyltTAMDT0FyVUsePH9OiRW/p448/1MqVy7R06b/1\n2Wcfa8WKpTp//rwWLVoiSRo+fLC6dLlNCQlnNXz4cHXoEK7HXlymfV+tV5uIJ5Ry+pTqdbpDbSJG\n6ZOJQ3Tu2CE17/Womvd6VJIU2SJU8fEpeR7//fdXqXv3HnmW+/n55xvvwYP7NX36ZJUpU1YLFrym\nxMQE+fsH6K23Xtevv+5S06Y3atiwkTKZTAY+SwDgmZJjT+iuKYt04JuPtfujFfrP5x/rnXfevWoN\nGDRoiFq2bK1PPvlI69a9ryeeGKNTp07qjjvu1qhRT2no0IE6fPigHn10sB59dHCuxwsK8lNiYto1\n48qvBtSpU08//rhFDRs20rZtW5WYmCBJjsbqzJkz+umn7Roy5PGiPi0AUOoxLLCUatiwsUwmk0JC\nQlW3bn1ZLBYFB4fo8OFDOnHiuJ54YpieeGKY0tLOKzb2lCpUCNHKlSv18MMPa+/G1cpMuXiF0Lec\nvyrUvDhu3q9CRWWlnb/mYy9atFA+Pj66556eBY63fv0GWr58le64424tXPii7Ha74uNP65577tOC\nBa/pwIH9+vHH/zj3ZACAlwmt00Amk0l+QSEKrlFXdpNZtWpV05Ejh3Xq1AmNHTtSY8eO1IULGcrI\nSFT9+jW1YcNaPfXU41q3brXSMy6+1vv7+6tevYvD/CpWrKjU1FTDY42IGKSjR49o1KihOnfurOx2\nu+NvCQnn9OyzY/T0088qMDDI8McGgNKGO1ellMViyffn5OQkdet2u8aNm5Br/Zkzp6pDhw4aMOBh\nPf7a+zq+82IjY7psW+nihBO71i/Pd1hg7dp19NZbrysxMUGRkc8XONatW7eoTZt2slqt6tKlm9at\nW6PAwCBVqlRZVatWkyS1bn2zjhw5rPDwWwr3RACAFzKZ/yrPZrNFVrNJaw8n6/S5RNUOv01Nhoxz\n/P1rST9MnqGwejep2T976ei2b2X542dJueuHdLEGLF++JN9hgSEhVZyKtXz58po69eKkRseOHdXP\nP/8k6eIkSWPHjtaQIcPVpk07p/YNAO6G5qqU8w8oo7JlfRQWVl6BgeXUtGlT7d4drYAAq8qWLasZ\nM2bomWeeUXp6qmrXriW73a5jP/0ge07OFfd5pWGBu3b9ot9+26t58xYUakanDRvWyWazqVOnztq7\nd4+qV68pq9WqKlWq6vjxY6pevYb27/9dt92Wd5ghAKDgQuo0UOzenbJlZsjiW0bbly9Q6/7DlZmS\npPKVqjpqgH+QzxX3UZRhgfnZsGG9cnKy1bNnb3366cfq0KGjpIuTGvXt21/t23dwar8A4I5orko5\nq8WsX89maHb0GR0/nKyzZSqoctdb1O3+vjKZLKp5c0e9/HuqLK3v1JiJU9WsTnXVDr9PW998QSd3\nbb/2A1xm/fr3dfp0rEaPvjgu/rrrAjVz5lwtWDBfDz7YTz4+Ppo6daLOnTurjIwM7dv3m8aOjdQT\nTzyt2bOnac2adx1TsUsXJ7qYO3eWLlzIVO3addShQyfDnx8A8CYBIZVUq20XbZw6wlEDrL5l1KDb\nfdq+7GUFhFVWox699d9lc/Xf/24r1L4/+eRDff75Rh06dEAzZ/5LNWvW0vPP/+uaNaBjx1s1YcI4\nffnl56pVq7aGDh2hjIwMff75pzp+/Jg+/vhDSVL37nfovvvud8XTAgClhsl++eDoQshvEgR3VJSr\ndc4IDPaXr7VwH3WbHX2mwOtGtggt9Pql8VgW93FxFU/JQyKX0sqdcgkLK19ij23U69yVnu+wsPIu\nf6125Wu7O/0/Kgzyci/k5X48NbegID/5+FiuvWI+nL5zFRBQRlarcw9amlgsZgUF+RXb4/lYzYUu\nkK5ky7EX6g1PVrZdusqQQ6MU93FxFU/JQyKX0sqTcgEAwN053VylpmYaGUeJKe6OuySv3ObHajYV\n/mroOdc/X55yJcRT8pDIpbRyp1xK2+sfAABG4zNXKJTC3umSpAu2HCUlXHsKeAAAAMCd0VyhUAp7\np0ty/dBGAAAAoDTgSzLk2k0AACAASURBVIQBAAAAwAA0VwAAAABgAJorAAAAADAAzRUAAAAAGIDm\nCgAAAAAMQHMFAAAAAAZgKnYAADxMYb+TMCvb7sJoAMB70FwBAOBhCvudhHwfIQAYg2GBAAAAAGAA\nmisAAAAAMADNFQAAAAAYgOYKAAAAAAxAcwUAAAAABqC5AgAAAAAD0FwBAAAAgAForgAAAADAADRX\nAAAAAGAAmisAAAAAMIC1pAMAAMDVAgLKyGq1FHk/FotZQUF+BkRUuthy7AoLK1/g9bOy7VJOjgsj\nMoanHi/yci+empfkublZLM7ff6K5AgB4vNTUTEP2ExTkp8TEtDzLC9OYlEZWs0mzo88UeP3IFqGK\nP5f3eShtrnS83B15uRdPzUvy3NyCgvxkNjt3QY7mCi5X2CuiF2w5kt3uwogAAAAA49FcweWcuSKa\nlZXtwogAAAAA4zndXBk1fr2keepYUXfnKcfFU/KQyKW08qRcAABwd043V0aNXy9pxT1W1N3H5ReX\n7OwcjxjD60ljkcmldHKnXHj9AwB4OqZiBwAAAAAD0FwBAAAAgAForgAAAADAADRXAAAAAGAAmisA\nAAAAMADNFQAAAAAYgC8RLqLAYH/5WulRAQDew5ZjL/DU+hdsOUpKOO/iiACgdKC5KiJfq1mzo88U\neP3IFqEujAYAANezmk0Frn3UPQDehFsuAAAAAGAA7lyh1LHl2OXjY2HICQAAANwKzRVKncIMN5EY\ncgIAAIDSgWGBAAAAAGAAmisAAAAAMADNFQAAAAAYgOYKAAAAAAxAcwUAAAAABqC5AgAAAAAD0FwB\nAADg/9u77/go6vyP4+8tSTCFJKTRe5EOKgiKFCWiHpY7ShDBclg4RCyABFBAPRAQRIQDKSoceoog\nYoNTUbAcgiBNQAFBSuhpJIGQkOz8/uDHSkhPZrPZzev5ePB4ZHe+u/P5fGd3vvthvjMDwAQUVwAA\nAABgAm4iDAAAXCbLYSgiIqjI7TOzHDqTdNaFEQGA61BcweMxcANA+WW3WjR5a3yR28e2DXdhNADg\nWhRX8HgM3AAAACgPOOcKAAAAAExAcQUAAAAAJqC4AgAAAAATlPicq8BAP9ntNjNjcQubzaqQEH93\nh4EyVlbb3Js+X+RSPnlTLgAAeLoSF1dpaRlmxuE2ISH+Sk4+V+LXF+cqdSg/SrPNi6O0n6/yhFzK\nJ0/Khf0lAMDbMS0QAAAAAEzApdivEBwaIF87NScAAACA4qG4uoKv3co9kwAAAAAUG4doAAAAAMAE\nFFcAAAAAYAKKKwAAAAAwAedcAQCAciPLYRTrsv2ZWQ6dSTrrwogAoOgorgAAQLlht1q4sBQAj8W0\nQAAAAAAwAUeuAABeLzDQT3a7rdTvY7NZFRLib0JEMFN+28Rbtxd5eRZvzUvy3txstpIff6K4AgB4\nvbS0DFPeJyTEX8nJ53I9X5xzhGC+vLaJlP/28nTk5Vm8NS/Je3MLCfGX1Vqy/5BjWiAAAAAAmIAj\nV6hwuBIVAAAAXIHiChUOV6ICAACAKzAtEAAAAABMQHEFAAAAACaguAIAAAAAE3DOlYczHA6tX/iK\nko4ckM3uoz7TJ0oK1oa3X9WpfTvl43fx3gMt7uyv6q3a6etpscpITVH7+4cpqklLSdKaV0ap49+H\nKyAsMsd7p546rrWvjdVdk95yPjdr1iztTvNRs9t6a9nQXgoIi5TFalN2Vqaqt2yna/o+otRTx7Xy\n2YEKr3e1DBnaWyVAIbfdr8hGLcqsXwAAuceIjg+PVEiNOrnGiA5PDVZ2QJNSjxFbl70pv6DgHGPE\nruBK+iPpbL5jhM3uo7Z9Hy7xGFHYRYquXMZFigC4ktcXV8GhAfK1F3yAzpPvT3J48/fKPJemni/N\nU8qJOE2dOlX1Bk/UhfPpuvHRWIXVbexse3T7RkU1aaUGN/XQlvfnK6pJS3377beqUqdhrkGzqKJH\nT5dPJX8ZDoe+mPiUTv62Xf5VIhVcvbZuHz9bktQ/7Jz6PPSouo+coqCoGqbkDQAo3JVjxMbFMxU9\n6pVcY0TXtuH6cNHnucaII1vXl3qMeL5jbb3886l8x4iUE3H6elpsiccILlIEoDzx+uLK12716p1u\nyok4RTRsJkmqXLWmfjl2THUc2bqQnvuGbudTz+iq4CryDwnX+dRkORzZWrx4sVo+8kKp47BYrQpv\n0FQpJ+LkXyXnIFy7dm21uLO/fvn0Xd3w8LOlXhcAoGiuHCPS4k/IUYwxYveqD3Tz8JdLHUdBY0Tl\nqjUZIwB4Da8vrrxdaK362rVqqZrd0VepJ+J05MgRXZNyRlkZ6dr24dvKTEuVf1iEOjz4tALCInV0\n2wadOX5YAWFR2vfNZ+r5l7/o/Y+XKD0pXk179FZYvcY53v/MscNa/cJQ52NbyinVjO6bK46szAwd\n37VFDW7qkWecYXUbad83n5qbfBnhvlgAPNWVY0TaqWPKyGOMGDz9pTzHiPo3RmtHMcaItNPH1bzn\nvbni8OYxAgAuR3Hl4Wq27aiTe3/R6gmPK7R2A9WvX1+GDDW55W6F1Kyn4Oq1tf2jxdq6bKGuf+Ap\n7Vv7mTYsmqF2/Ydoy7KFqtPtCVk271WHh57Rupnj1P3ZqTne//KpG5IU8MN72pT25/KvXh4ui9Um\nSWpyy10KrVVfqaeO54rTkZXlbOdpmHICwFNdOUYE16iT5xgxa9YsRd3xWK4xovU99yv11LEijxFb\nl72ZY/lXLw/X3uBKOpx6wWvHCAC4HMWVF7g25lHn32tG9tNVlUNVp30X53N12nXW+jenyWK16qYh\nz0mSti5bqJZ39texY8cUGF5Vdr9KeU4TKcylc64KE3/gN1Wp26jY7w8AKJ3Lx4jlw/rkOUbsWTpT\nLXrmHiPS4k+Ueox4vmPtQv+DijECgLfgUuweLvHQPv3wxiRJUty2DWrWrJksVqvWvPKs0uJPSJKO\n796q0Fr1na85l3haKSfiVK35tQoPD9fZhJPKyjgvm6+vS2I8fPiwdn2+VM3/EuOS9wcA5O3KMSKs\nXpM8x4hGjf4sbC4fI64KruLyMSLlRBxjBACvUeIjV4GBfrLbOYTvbqG1GshwOPTZ84/K1z9Iy+a+\nqgWHDTW9tZfWvjpWdr+rZK9USZ0Gj3W+ZtuKt9Wm9yBJUvv27RX/+nytfvEJtf7bA6bFdWkevsOR\nrZ2V/dTpH2MVGF7VtPcv70JCLh7Ns9mszr89HbmUT96UC8x35Rhx6cjUlWPEq/+argWHDUk5x4iq\nzdpq16qlLh0jLFZrhRsjAHivEhdXaWkZZsbhMp58mfWiuHyqnySFhYVJh+NVo/X1qtH6+jxfc/nV\nmOx2u6JHTcuzXVBktRz3L5GkJ554wjm9o8/sD/N93cBFa5yPY9uGF+ucJW+QnHxx+kxIiL/zb09H\nLuWTJ+Xi7fvj8ujKMeKSK8eIS2OHlHOMsNqKN0a07TPI+XdRxwgA8CZMCwQAAAAAE3BBCwAAUGFw\new0ArkRxBQAAKgxurwHAlZgWCAAAAAAmoLgCAAAAABNQXAEAAACACSiuAAAAAMAEXNACAAAgH1xd\nEEBxlFlxdeDA74qNHa6YmP7q1Ssmx7JPPvlIn332sWw2qxo0aKzhw0dpz57fNHr0cNWoUVOS1KBB\nQz399LM6dOigpk6dKIvFolq1amv48FjZ7dSIKD+uHIgv/Z2enq7Y2FglJCQoIyNDQ4YMUbdu3ZwD\n8aZNGzV//r9ktdrUseONevDBhyXl/d3hewCYo6CxKb/vJCqWol5dMOnIAX39yig99dgg9ehxd55t\n3nhjtnbu3KHZs+fL4XDolVde1h9/7JfdbtfIkWNUp05dSdLy5e9r1qwZWr16rfz9/c1MB4CLlcmv\nsfT0dM2Y8YquvbZ9rmXnz5/X119/qTlzFsput2vYsMHauXOHsrKy1LXrLXryyeE52s+d+7oGDHhQ\nHTveqEWLFuqbb9bo1ltvK4s0gCLJbyA+sH6Nzlapr5YPPq+00yf07ISn1CukpfMyvzNnTtP06bMU\nERGpIUMeVpcuN6tq1Wp5fnf4HgClV9DYJOX9nWzbtkUZRwlPcOF8uja8/aqqtbgu3zZ//HFA27dv\nkc128afX999/q7Nn0/TGG2/p6NE4zZw5TVOnvqbVqz9TQkKCwsMjyip8ACYqk3OufHx8NG3aTIWH\n575XRKVKlTRz5lzZ7XadP39eaWlpqlIlTOfOncvzveLijqhZs+aSpPbtO2jTpg0ujR0wS/0buqvl\nXfdJks4mnJR/2J8D59GjcQoKqqyoqKqyWq3q2PFG/fzzT/l+d/geAKVX0NiU33cSyIvNx0fRsdPl\nH5r/PbFmz35NjzwyxPk4Lu6wmja9uB+vUaOmTpw4ruzsbHXp0k2PPfa4LBaLy+MGYL4yKa7sdrv8\n/CoV2GbJkkWKiblbN9/cXTVq1FR6+jnt2LFNw4cP0+OPP6ItWzZLkurXb6j163+QJP300wYlJia6\nPH7ATJ89/5i+nfWCrr//SedziYkJCgkJdT4OCwtTQkJCvt8dvgdA6RU0NuX3nQTyYrXZZff1y3f5\nqlWfqk2ba1StWnXnc/XrN9RPP/2o7OxsHT58UMeOHdWZM8ny9w8oi5ABuEi5OUlj4MAH1bdvP40Y\n8aRatWqjhg0b66GHHlanTl10+PAhPfXUEC1dulKjx4zWxH++qDVrVqt9+/by8bEW60RTwN16vjRP\nCQf36rt/vai7pyxWlsNQcPBV8vOzOz/LgYGVFBDg53wcEOCnwMBKiogIUmaWQ48//qSmT5+s1as/\nU5s218gwDHemBHidK79TfMVQUikpZ7Rq1ad67bU5On36lPP5jh1v1C+/bNfQoY+oQYNGqlOnHvty\nwAu4vbhKSTmjAwf2q02ba+TnV0kdOtygX37Zrvvue0B169aTJNWuXUdhYWE6ffqUWre+WvUGT5Qk\n7dm+UacrHS7wRNNL57MA7hZ/4DdVqhyqwPAohdVtLEd2ts6nJMtujdCKeF9tP3Tc+Vneuu0P+QVW\n/vPx8XPyS/NR3NZ4xbYNV1RUVU2d+pokaePGH5WQUPjJ1gCKLiIiUomJfx6pOn36VJ7TB4HC/Pzz\nJiUnJ2nIkId14UKmjh49qtdfn65hw4br0Uf/nCbYt+/dCg2t4sZIAZjB7fe5ysrK0sSJLzjPsfr1\n112qXbuOPvvsYy1b9r4kKSEhXomJiYqIiNTrr7+uI1vWS5L2rftcta7p5LbYgeI4+es27fr8PUlS\nenKiss6nq1JQsCQpKLKaLqSfVeqp43JkZyluy/9Uo1XeJ9lL0ptvznNOC1y16hPdeGNn1ycAVCDV\nqlXX2bNndfz4MWVlZWn9+h/Url0Hd4cFD9StW3e9884yzZ+/SJMmTVPjxk00bNhw7du3V5MmvSBJ\n2rBhvRo3vlpWq9t/lgEopTI5cvXbb79q9uwZOnHiuOx2u9au/VqdOnVWtWo11KVLNz300MMaNmyw\nbDabGjZspE6duig1NVUvvvic1q37WpmZmRoxIlY+Pj7q2bOnlg59Rjs+XqJqzdqq1jU3lEUKQKk1\nif6r/vfGy1o1/h/KupChDn9/Rr9/t1pfJVaXwtuq46CR+nbWeElS3Y63KLh6bcUf+E2blsxW2unj\nstjtOrRxnQYvekPR0T300kvjtGTJ27rmmut0ww38JwNQXIWNTSNGxGrChLGSpJtvjlbt2nXcHDHK\nq8v31Ys3+emLL77QzTffrJo1ayo6OtrZLiMjQL6+F6eAh4W11SefLNPjjw9S5cqVNWXKFIWFBWnu\n3Llav369EhMTNHr002rTpo2effZZSdxDC/AEZVJcXX11U82ePT/f5XfccafuuOPOHM9VrlxZ06a9\nnqtt/fr1defEhabHCLia3ddPXYZNyPV8dNtw/bw1XlWbtlHPl3J+T8LrX63bx8/O8Vxg5WBde22I\nVq78qEjrZTAG8lbY2NSmzTWaN+/tMowInuryfXVs23BN3hqvk5JOSvo5x6kLldT8mRnOKd8hMSP0\nwf+3X3DYkA7HSx36qHmHPmr+/69wSM72nOoAlH9uP+cKQPEU9YaWlzAYAwAAlA23F1fBoQHytTPH\nGAAAoCBZDsN5FdmiXCmZmQtA2XN7ceVrt/K/8AAAAIUo7syFEa3DinW7GooxoPTcXlyVxv5NP+jj\nl5/V6YP78m0zupjvSXtz25fFOjyhfUTdRrp79FQ1aFf2F564/H86i4LBFcjthx++06hRz2jfvr2m\nvJ8n7LfMal+eYnFFe3fu3wvDNHKg7Hl0cfXRxOFKOHzA3WEAhTp9cJ8+mjhcI1ZuLPN1M7gCpTdi\nxJM6cGC/u8NAOeTO/TuA8sejiysA5ivoSFdez3OkCwAqpuKeN894gYrAo4urv46drk8mj9KpP8yZ\npgG4SmS9xrordoq7wygS5vQDuU2bNlOxscO1d+8ed4eCcsaT9u+FKe40ckmmjxeXL7/gMORjtRT5\n/RlfUB54dHHVoF0nPf3h/wpsc+l+E0VFe3Pbl8eYylt7T+fqYqy4g2tR21+KgcEYRdGpU2f98MMm\nhYT4Kzn5XK7lERFB5Wq/Up7al6dYyqK9J3P1NPKSvL+rxpeKVrhxlLHsWAzDMNwdhDutW7dOXbt2\ndXcYpiCX8sdb8pDIpbzyplw8gbf2N3l5FvLyLN6al+S9uZUmrwp/g6lvv/3W3SGYhlzKH2/JQyKX\n8sqbcvEE3trf5OVZyMuzeGtekvfmVpq8KnxxBQAAAABmsE2YMGGCu4Nwt7p167o7BNOQS/njLXlI\n5FJeeVMunsBb+5u8PAt5eRZvzUvy3txKmleFP+cKAAAAAMzAtEAAAAAAMAHFFQAAAACYoEIVV3v3\n7lX37t31zjvv5Fp2zz33aODAgc5/J0+edEOERTN16lTFxMSoV69e+vLLL3MsW79+vXr37q2YmBj9\n61//clOERVdQLp60TdLT0/Xkk09qwIAB6tOnj9auXZtjuSdtl8Jy8aTtIknnz5/XLbfcohUrVuR4\n3pO2ySX55eJp28RTFDRmeOLn55KC8tqwYYP69u2rfv36afTo0XI4HG6IsGQKyuuS6dOna+DAgWUY\nVekVlNfx48d17733qnfv3ho3bpwboiu5gvJ69913FRMTo3vvvVcTJ050Q3Ql502/0S5XUF6evN8o\nKK9Lir3fMCqIs2fPGgMGDDCee+45Y8mSJbmW33333W6Iqvh+/PFH4+GHHzYMwzASExONLl265Fh+\n++23G8eOHTOys7ONmJgYY9++fW6IsmgKy8VTtolhGMbnn39uzJ8/3zAMw4iLizNuvfXWHMs9absU\nlosnbRfDMIxXX33V+Nvf/mZ8+OGHOZ73pG1ySX65eNo28QSFjRme+PkxjMLzio6ONo4fP24YhmE8\n8cQTxrp168o6xBIpLC/DMIx9+/YZMTExxoABA8o4upIrLK9hw4YZX375pWEYhjFhwgTj6NGjZR1i\niRSUV2pqqtGtWzfjwoULhmEYxkMPPWRs3brVHWEWmzf9RrtcYXl56n6jsLwMo2T7jQpz5MrX11cL\nFixQZGRknsvPnvWMu1C3a9dOM2fOlCQFBwcrPT1d2dnZkqQjR44oODhY1apVk9VqVZcuXfTjjz+6\nM9wCFZSL5DnbRJLuuOMOPfLII5Iu/k9iVFSUc5mnbZeCcpE8a7vs379fv//+e64bAXraNpHyz0Xy\nrG3iKQoaMzzx83NJYWPhihUrVLVqVUlSlSpVlJSUVJbhlVhheUnS5MmT9fTTT5dhVKVXUF4Oh0M/\n//yzbr75ZknS+PHjVb169bIOsUQKysvHx0c+Pj46d+6csrKylJ6eruDgYDdEWXze9BvtcoX9XvPU\n/UZheUkl229UmOLKbrerUqVK+S5PTk7W8OHD1a9fP82YMUNGOb2Ios1mk7+/vyRp2bJl6ty5s2w2\nmyTp9OnTqlKlirNteHi4Tp8+7ZY4i6KgXCTP2SaX69evn0aMGKExY8Y4n/O07XJJXrlInrVdpkyZ\notjY2FzPe+I2yS8XybO2iacoaMzwxM/PJYWNhYGBgZKkU6dOaf369erSpUtZhVYqheW1YsUKtW/f\nXjVq1CjDqEqvoLwSExMVGBio119/XQMGDND06dM95rtfUF5+fn56/PHH1b17d918881q06aN6tWr\nV8YRlow3/Ua7XGG/1zx1v1FYXiXdb1SY4qowTz/9tF544QUtWbJEu3fvznfeZXmxZs0aLV++PMcc\n67x2qhaLpSzDKpG8cpE8b5tI0vvvv6+5c+dq5MiRzu3hqdslr1wkz9kuK1euVJs2bVSrVq1cyzxt\nmxSUi+Q528RbeNrnp7gSEhI0ePBgjRs3TqGhoe4Op9SSk5O1YsUKPfTQQ+4OxVSGYejkyZPq1auX\nFi9erN27d+vbb791d1illpaWpnnz5um///2v1qxZo23btum3335zd1jF4k2/0S6X3+81ybP3G3nl\nVZr9BsXV/+vfv78CAwPl4+Ojrl27as+ePe4OKV/ff/+93njjDS1YsEBBQUHO56OiohQfH+98fPLk\nSUVERLgjxCLLLxfJs7bJzp07dfz4cUlS06ZNlZ2drcTEREmet10KykXynO2ybt06ff311+rbt6+W\nLVumOXPmaP369ZI8b5sUlIvkOdvEW3ja56c40tLS9Mgjj+jJJ59Up06d3B2OKTZs2KDExETdd999\nGjp0qHbt2qVJkya5O6xSCw0NVbVq1VS7dm3ZbDZ17NhR+/btc3dYpbZ//37VqlVLVapUka+vr667\n7jrt3LnT3WEVmTf9RrtcQb/XPHm/kV9epdlvUFzp4qH1Rx55RBcuXJAkbdq0SY0aNXJzVHlLTU3V\n1KlTNW/ePIWEhORYVrNmTaWlpSkuLk5ZWVlau3atbrzxRjdFWriCcvGkbSJJmzdv1ltvvSVJio+P\n17lz55z/c+Np26WgXDxpu7z22mv68MMP9cEHH6hPnz4aMmSIbrjhBkmet00KysWTtom38LTPT3FM\nnjxZDzzwgMdM6ymK2267TatWrdIHH3yg2bNnq3nz5rmmO3siu92uWrVq6eDBg5KkXbt2ecz0uYLU\nqFFD+/fv1/nz52UYhnbu3Km6deu6O6wi8abfaJcrKC/Jc/cbBeVVmv2G3RXBlkc7d+7UlClTdPTo\nUdntdn3xxRe6+eabVbNmTUVHR+v6669XTEyMfH191axZM/Xo0cPdIedp1apVSkpK0lNPPeV87vrr\nr1eTJk0UHR2tCRMmaPjw4ZIuXpigPO9oC8vFU7aJdPH8pLFjx6p///46f/68xo0bp5UrVyooKMjj\ntkthuXjSdrnSihUrPHKb5OXyXDx5m5RXhY0Znvr5KSivTp06aeXKlTp06JCWL18uSerZs6diYmLc\nHHXhCttenqqwvMaMGaPx48crIyNDjRo1cl7corwrLK9Bgwbp/vvvl81mU9u2bXXddde5O+Qi8abf\naJcrKC9P3m8Utr1KymJ4ytmPAAAAAFCOMS0QAAAAAExAcQUAAAAAJqC4AgAAAAATUFwBAAAAgAko\nrgAAAADABBRXAAAAAGACiisAAAAAMAHFFQAAAACYgOIKAAAAAExAcQUAAAAAJqC4AgAAAAATUFwB\nAAAAgAkorgAAAADABBRXQCFWrFihr776yt1hAAAAoJyzGIZhuDsIAAAAAPB0dncHALjKnXfeqbff\nflvh4eFauXKl9uzZo1GjRuVqN3DgQF1//fX63//+J6vVqnvuuUcfffSRbDabFi1apDlz5ig0NFSN\nGjXSu+++K4vFogMHDqhHjx4aOnSoBg4cqOeff16NGzfWO++8o6SkJD344IN66qmnlJmZqczMTI0b\nN07NmzfPM84TJ05ozJgxunDhgiwWiyZOnCiLxaLY2FjVqlVLe/bsUdOmTTVx4kSdPHlSzz33nDIz\nM2Wz2fTPf/5T1atXd3VXAgAAoAiYFgiv1b17d3333XeSpPDwcCUkJOTbNiIiQu+9956ys7N15swZ\n/ec//1F2drb27t2bo92OHTs0efJkvf/++1qyZEm+7/fjjz8qKipKS5Ys0bRp0xQfH59v25kzZ6p3\n795asmSJ+vfvr9mzZ0uSdu3apWeeeUbLly/Xt99+q5SUFM2cOVMPPfSQFi9erAceeEBz5swpTpcA\nAADAhSiu4LWio6O1bt06SdKxY8dUv379fNu2atVKkhQZGalmzZpJuliQpaam5mjXrFkzXXXVVQoI\nCChw3W3atNG2bds0btw4HTp0SF26dMm37c6dO9W+fXtJ0nXXXafdu3dLkmrXrq2IiAhZrVZFRkYq\nNTVVW7du1axZszRw4EDNmzdPycnJBXcCAAAAygzTAuG1mjVrpoMHD+rChQtau3atRo4cmW9bm82W\n599XnpJotxf8lcnKypJ0sUj7+OOPtXHjRr333nvatm2bhg4dmudrLBaLcz0Oh0NWqzVXHJdi8fHx\n0cyZMxUZGVlgHAAAACh7HLmCV+vYsaPeffddVapUqcAjV6URGBio06dPS5K2bNkiSVq/fr3Wr1+v\nTp066fnnn9fOnTvzfX3Lli21ceNGSdKmTZvUokWLfNu2bt1aa9askXRx6uGnn35qVhoAAAAoJY5c\nwatFR0frscce0yeffOKydcTExOjFF19UnTp1VLt2bUkXp/SNHDlSCxculMVi0bBhw/J9/bBhwzR2\n7Fh98MEH8vHx0aRJk3ThwoU82w4dOlRjxozR559/LovFopdfftklOQEAAKD4uBQ7AAAAAJiAI1eo\nEI4dO5bnZdjbtWtX4FEls2RmZmrQoEG5nq9Xr55efPFFl68fAAAArseRKwAAAAAwARe0AAAAAAAT\nlHha4OnTqYU3khQY6Ke0tIySrgYFoG9di/51LfrXdcpr30ZEBLk7BAAAXMrlR67sdlvhjVAi9K1r\n0b+uRf+6Dn0LAIB7MC0QAAAAAExAcQUAAAAAJqC4AgAAAAATUFwBAAAAgAlKfJ+r9PTMIp00bbNZ\nlZ3tKMkqUAj6M0DhMwAAFrBJREFU1rXoX9eif12nvPatjw8X2gAAeLcSX4q9qJf5DQnxV3LyuZKu\nxusEhwbI1170A4aZWQ6dSTqb5zL61rXoX9eif12nvPYtl2IHAHi7EhdXKBlfu1WTt8YXuX1s23AX\nRgMAAADALJxzBQAAAAAmoLgCAAAAABNQXAEAAACACSiuAAAAAMAEFFcAAAAAYAKKKwAAAAAwAcUV\nAAAAAJiA4goAAAAATEBxBQAAAAAmsLs7AE8XHBogXzs1KgAAAFDRUVyVkq/dqslb44vcPrZtuAuj\nAQAAAOAuFFdeIC0tTS+8MFZpaWm66ip/TZjwT1WuHJyjzZtvztOGDetlt9s0ePAwtW7dRgcO7NeM\nGVMlSVarTaNGjVX16jU0f/4cbd26WQ6Hoc6du+q++x5wR1oAAACAR2E+mxf44IP/qG3bazV37pvq\n1Kmz3nlncY7le/f+pk2bNuqNN97SlCmv6Y03XpckvfXWPA0Y8KBmzZqnv/zlLr377mIdOPC7tmzZ\nrLlz39LcuW9q1apPlZBQ9CNzAAAAQEXFkSsT7Vv3uU78uk0ZqWeUFPeHro15VAfWf6XkuIPqMnS8\n4v/Yo35TvtGxc9mq3a6zWvS8V2cTTum7f70oSXJkZ+umf4xV5ao1tfzJvqp9XWf1fXm3KleurPnz\n52vevHlav359jnWOHz9eO3Zs0aRJkxQREaQ7et6uIYMH52hz5MgRNWlytWw2mypXrqyAgEAdP35M\nwcEhOnPmjCQpNTVFwcEhCggIVGZmhjIzM+VwOGSxWFWpUqWy6UAAAADAg1FcmSzlRJzumDBHe7/5\nVDs+XqK7Jr+t39et0vaV/9aF9LNat+I9Td4ar8/HDVbdDt2UfiZJbXo9pGrNr9XetZ/pt68+UvuB\nTyj11DE17Hybpt4zQZ3+8leN+niDwjr0UfMOfXKsb3mqtDfupBbHGfJNjNfTLSKUlJSgiIggZ5vr\nrmuld999W4GBdp09e1b79++TYZzXqFEj1KtXLy1evFDZ2dlasODfCgoKUrdu3dW7951yOLL14IMP\nKyAgsKy7EQAAAPA4FFcmC6/fRBaLRf4hYQqt3UBWq01XBVdR0uH9cmRn6f7779fh1Au6cP6c0k6f\nUGBENW1c+W9tXfamMs6mKrxeE0mS71UBqlKnoSTJv0qkLpw7m+86DRnOv20W6WyWccVFNkIUesNf\nFN1ngIKiqsu3egMt3pOkvXP/rWeeeUYdO3bThx8u1aJFC/S3v/XVd9+t1QcffKysrCwNHvx33XLL\nrQoNreKS/gIAAAC8BcWVySzWP7vUarU5/85IS1G9G7pryZypOQqf7+dOVI1W7XV19F91cMNaHdny\nv4vvY/vztZJkGIa2f7RYx3ZsyvF8x0HDFRAaofTkBPn6B+rkyZO6KjQsV1zNbuutZrf1liR99vyj\nCoyoplN7ftFNLz+nrCypXbvrNWXKRP322241a9bCORWwQYOGOnBgv669luIKAAAAKAjFVRkJq99E\nJ3ZtUXp6ugzD0MbFM3Vd/38oI/WMgqJqyDAMHd78vQyHI9/3aP3XB9T6r7mv3Fe9VTv9sWGt2vzt\nQX355Zeq0bpDjuXnU5L03Zx/KnrUNCXH/SHDYcg/JEyVq9bUjh071KzZNfr1192qWbOWatSopQ8+\neE8Oh0MOh0MHDvyu6tVrmN4fAAAAgLehuCojgWFRqnt9N9133306ed5QnXY3ye7rpya33K2Ni15T\nYERVNe3RW+sXTNHR7RuL9d7Nbu+j72a/qFXj/6Fm1cPUcmCsJGnj4tfU7Pa+CoqsrrA6jfTp2EHy\n8fNX58eflyRdd9/jWrjwNWVmZsnX11fPPvucqlatqvbtO2jIkIdlGIbuvPMeVatW3fT+AAAAALyN\nxTAMo/BmuZ0+nVqkdiEh/kpOPleSVXiEiIigYt9EuLy1L+q2rGi8/bPrbvSv65TXvr38QjsAAHgj\n7nMFAAAAACaguAIAAAAAE1BcAQAAAIAJSnxBi8BAP9nttkLb2WxWhYT4l3Q1KANsn7zx2XUt+td1\n6FsAANyjxMVVWlpGkdqV1xOrzeINJ2h78/YpDW//7Lob/es65bVvvWF/CQBAQbgU+xWCQwPka2e2\nJAAAAIDiobi6gq/dWuxLmQMAAAAAh2gAAAAAwAQUVwAAAABgAoorAAAAADABxRUAAAAAmIDiCgAA\nAABMQHEFAAAAACaguAIAAAAAE1BcAQAAAIAJKK4AAAAAwAQUVwAAAABgAoorAAAAADABxRUAAAAA\nmIDiCgAAAABMQHEFAAAAACawuzsAuFeWw1BERFCR22dmOXQm6awLIwIAAAA8E8VVBWe3WjR5a3yR\n28e2DXdhNAAAAIDnYlogAAAAAJiA4goAAAAATEBxBQAAAAAmoLgCAAAAABNQXAEAAACACSiuAAAA\nAMAEJb4Ue2Cgn+x2W6HtbDarQkL8S7oalEMVZXvy2XUt+td16FsAANyjxMVVWlpGkdqFhPgrOflc\nSVdT5opzQ92KypO2Z2l42mfX09C/rlNe+5b9KwDA23n9TYSDQwPka2f2IwAAAADX8vriytdu1eSt\n8UVuH9s23IXRAAAAAPBWHNIBAAAAABNQXAEAAACACSiuAAAAAMAEFFcAAAAAYAKKKwAAAAAwAcUV\nAAAAAJiA4goAAAAATEBxBQAAAAAmoLgCAAAAABNQXAEAAACACSiuAAAAAMAEFFcAAAAAYAK7uwOA\nZ8lyGIqICCrWazKzHDqTdNZFEQEAAADlA8UVisVutWjy1vhivWZE67BiFWQUYwAAAPBEFFdwueIW\nZLFtw10YDQAAAOAanHMFAAAAACaguAIAAAAAE1BcAQAAAIAJKK4AAAAAwAQUVwAAAABgAoorAAAA\nADABxRUAAAAAmKDE97kKDPST3W4rtJ3NZlVIiH9JV4MKqjx8Zvjsuhb96zr0LQAA7lHi4iotLaNI\n7UJC/JWcfK6kqym1iIggt60bJefOz8wl7v7sejv613XKa9+yPwYAeDumBQIAAACACSiuAAAAAMAE\nFFcAAAAAYAKKKwAAAAAwAcUVAAAAAJiA4goAAAAATEBxBQAAAAAmoLgCAAAAABNQXAEAAACACSiu\nAAAAAMAEFFcAAAAAYAKKKwAAAAAwgd3dAQBXynIYiogIKnL7zCyHziSddWFEAAAAQOEorlDu2K0W\nTd4aX+T2sW3DXRgNAAAAUDRMCwQAAAAAE3jckavg0AD52j27JjQcDq1f+IqSjhyQze6jjg+PVEiN\nOtrw9qs6tW+nfPz8JUkt7uyvzOa36cvJw5WRmqL29w9TVJOWkqQ1r4xSx78PV0BYZI73jouL0ydj\nhuiuSW85n9u67E35BQWr2W29tWxoLwWERcpitSk7K1NXRXeROt+n1FPHtfLZgQqvd7UMGbLZfdS2\n78OKbNSi7DoGAAAA8GAeV1z52q0eP2Xs8ObvlXkuTT1fmqeUE3HauHimoke9ogvn03Xjo7EKq9vY\n2Xbjxo2KatJKDW7qoS3vz1dUk5Y6snW9qtRpmKuwKqro0dPlU8lfhsOhLa+PVJXIFvKvEqng6rV1\n+/jZkqSUE3H6elqsuo+coqCoGqbkDQAAAHgzzz4E5KFSTsQpomEzSVLlqjWVFn9CDke2LqSfy9U2\nOTlZVwVXkX9IuM6nJsvhyNbuVR+o5V0DSh2HxWpVy5YtlXIiLteyylVrqsWd/fXLp++Wej0AAABA\nReBxR668QWit+tq1aqma3dFXqSfilHbqmDJSzigrI13bPnxbmWmp8g+LUIcHn1bVqlWV+v12nTl+\nWAFhUdr3zWeqf2O0dny8ROlJ8Wrao7fC6jXO8f5njh3W6heGOh+nnT6u5j3vzRVHVmaGft64UfUH\njswzzrC6jbTvm0/NTR4AAADwUhRXblCzbUed3PuLVk94XKG1Gyi4Rh0ZMtTklrsVUrOegqvX1vaP\nFmvrsoV6/rV/6tz8d7Vh0Qy16z9EW5YtVOt77lfqqWPq8NAzWjdznLo/OzXH+18+vU+6eM7V5b56\nebgsVpskaeh9fbW/Vn2lnjqeK05HVpazHQAAAICCUVy5ybUxjzr/Xj6sj66qHKo67bs4n6vTrrPW\nvzlNVqtVNw15TpK0ddlCtbyzv9LiTygwvKrsfpXynEpYmEvnXElSn7bh+Z7DFn/gN1Wp26jY71/W\nuC8WAAAAygOKKzdIPLRPu1cvU6fBYxS3bYPC6jWRxWrVmleeVYeHnlFgeFUd371VobXqO19zLvG0\nUk7EqW2fh3Xsl006+dt2ZWWcl83X1yUxppyI067Pl6rHc6+55P3NxH2xAAAAUB5QXLlBaK0GMhwO\nffb8o/L1D3IemWp6ay+tfXWs7H5XyV6pkjoNHut8zbYVb6tN70GSpKrN2mrXqqVa/eITav23B0yL\n69K5Wg5HtixWqzr9Y6wCw6ua9v4AAACANytxcRUY6Ce7vfDzcWw2q0JC/Eu6Gq9kuWyq3+VqtL5e\nNVpfn+drbnj4WeffVptd0aOm5dmuZs2aOe5xJUlt+wxy/t1n9od5vi4ospoGLlpTaOzeoiifST67\nrkX/ug59CwCAe5S4uEpLyyhSu5AQfyUnF/+8oPwU59waID9F+Uya/dlFTvSv65TXvmX/DQDwdtzn\nCgAAAABMQHEFAAAAACaguAIAAAAAE1BcAQAAAIAJKK4AAAAAwAQUVwAAAABgAoorAAAAADBBie9z\nBXiqLIdR5PvtREQEKTPLoTNJZ10cFQAAADxdkYurSZMmafv27bJYLBozZoyqVavnXJaRkaGpUyfq\n4ME/9OabS5zPHzjwu8aMGak+ffqpV68Y5/PLl7+vWbNmaPXqtfL39zcpFaBo7FaLJm+NL7Rd0pED\n+vqVUXrqsUHq0ePuHMu+/36dFi9+Sz4+Pure/Vb16hWjzz5bqf/+d5WzzZ49v+qrr77XL79s16xZ\nM+Tj46NWrdroscceNz0nAAAAuF+RiquffvpJhw4d0tKlS/X7779r9OjRmjPnLefyOXNmqnHjJjp4\n8A/nc+np6Zox4xV16NAhx3utXv2ZEhISFB4eYVIKgPkunE/XhrdfVbUW1+Va5nA4NGPGK3rzzXcU\nHBysESOG6aabuqpnz3vUs+c9kqStW3/WN9+skSRNmzZZEyZMVL169fXyyy/ql1+2q2XL1mWaDwAA\nAFyvSOdc/fjjj+revbskqWHDhkpJSdHZs2nO5Y899rg6d+6W4zU+Pj6aNm2mIiJyFlFdunTTY489\nLovFUtrYAZex+fgoOna6/EPDcy07cyZZgYGBCg0NldVq1bXXttPmzT/laLNo0UI9+OAgSVJCQrzq\n1asvSWrfvqN++mmD6xMAAABAmStScRUfH6/Q0FDn47CwMCUkJDgf+/sH5HqN3W6Xn1+lXM/n1RYo\nb6w2u+y+fpKkbOPiOVqX/jVqVFsZGed19myCQkIqaefObcrISHMuPxJ3QJGRUQoLu1iYVatWXdu2\nbZFhGNq8eaOSkhLdmRoAAABcpEjTAg3DyPWYI0+oKGyW3OdotRo0WvcPGykf/0AFhkdp3bGzSvz/\nNuc++lC3397T2Xb06Oc1c+Z0Wa1WNWrUWGfPcnEMAAAAb1Sk4ioqKkrx8X/+uDx16pTCwsJcFhRQ\n3lVt1lZ3vDBXkrT5vbkKjKjmXLZx40Y999xz8vX1lSRFRLTVf/7zjiTp/fffV0pKSo6rFXI1QgAA\nAO9QpOLqxhtv1KxZs9SvXz/t3r1bkZGRpk3vCw4NkK+d223Bs3z58nB1fvw52Xwr6cjP/1OLv9wr\nSTqXeFoBAQF6dVeKs+0Pb0xSs9v7KqRWPa3+z4e64eGROY6EjWgdVuRLw0sUYwAAAOVVkYqra665\nRs2bN1e/fv1ksVg0fvx4rVr1qQICAtWlSzc999wonTp1UocPH9LQoY/qrrv+ptq162j27Bk6deqE\nrFab1q79WpMmvaKPPlquTZs2KjExQSNGDFO7dtfKEf33Igcc2zb3BQYAs8Uf+E2blsxW2unj+vdm\nP2X4f6Za13VSUEQ11WnfRY1vuVNfTHxKdr+rdE3Mo6pUOUSSdC45QVWqVMnxXo269dT3cyfK7uun\nBp16KLRW/RzLi3pp+Ev4DgAAAJRPRb7P1YgRI3I8Dgur4fz7n/+ckudrZs+er5AQfyUnn3M+98AD\ng/TAA4OcjyMigor1wxIoC+H1r9bt42dLuljMXPkZrdu+q+q275rn66YtXJijfVSTVrp78tsujRcA\nAADux3w8AAAAADABxRUAAAAAmKDI0wIBlA9ZDoMLYAAAAJRDbi+u1q5dq1f//phOH9xXpPaji/n+\ntHdv+7JYh9ntI+o20t2jp6pBu07FfOeywQUwAAAAyie3F1ePPVb0wgooC6cP7tNHE4drxMqN7g7F\nFBzpAgAAKBtuL64AuFZxj3S5+r5bl9/brijrodgDAACewu3F1bx589Rv0GCd+mOvu0MBJEmR9Rrr\nrti8by9QEbi6GJNU4aY1Fvdm6RSUAAB4JothGIYrV7Bu3Tp17drVlauosOhb16J/XYv+dR36FgAA\n93D5pdi//fZbV6+iwqJvXYv+dS3613XoWwAA3IP7XAEAAACACVxeXHXp0sXVq6iw6FvXon9di/51\nHfoWAAD3cPk5VwAAAABQETAtEAAAAABMQHEFAAAAACaguAIAAAAAE7isuJo0aZJiYmLUr18/7dix\nw1WrqbD27t2r7t2765133nF3KF5p6tSpiomJUa9evfTll1+6OxyvkZ6erieffFIDBgxQnz59tHbt\nWneH5JXOnz+vW265RStWrHB3KAAAVCh2V7zpTz/9pEOHDmnp0qX6/fffNXr0aC1btswVq6qQzp07\np5deekkdO3Z0dyheacOGDdq3b5+WLl2qpKQk/fWvf9Wtt97q7rC8wtq1a9WiRQs98sgjOnr0qP7+\n97+rW7du7g7L68ydO1chISHuDgMAgArHJcXVjz/+qO7du0uSGjZsqJSUFKWlpSkwMNAVq6twfH19\ntWDBAi1YsMDdoXildu3aqVWrVpKk4OBgpaenKzs7Wzabzc2Reb477rjD+ffx48cVFRXlxmi80/79\n+/X777+ra9eu7g4FAIAKxyXTAuPj4xUaGup8HBYWptOnT7tiVRWS3W5XpUqV3B2G17LZbPL395ck\nLVu2TJ07d6awMlm/fv00YsQIjRkzxt2heJ0pU6YoNjbW3WEAAFAhueTI1ZW3zjIMQxaLxRWrAlxm\nzZo1Wr58ud566y13h+J13n//ff36668aOXKkPvnkE/YPJlm5cqXatGmjWrVquTsUAAAqJJcUV1FR\nUYqPj3c+PnXqlMLDw12xKsAlvv/+e73xxhtauHChgoKC3B2O19i5c6fCwsJUrVo1NW3aVNnZ2UpM\nTFRYWJi7Q/MK69at05EjR7Ru3TqdOHFCvr6+qlq1qm644QZ3hwYAQIXgkuLqxhtv1KxZs9SvXz/t\n3r1bkZGRnG8Fj5GamqqpU6dq0aJFXBTAZJs3b9bRo0c1duxYxcfH69y5czmmEKN0XnvtNeffs2bN\nUo0aNSisAAAoQy4prq655ho1b95c/fr1k8Vi0fjx412xmgpr586dmjJlio4ePSq73a4vvvhCs2bN\nohAwyapVq5SUlKSnnnrK+dyUKVNUvXp1N0blHfr166exY8eqf//+On/+vMaNGyerldvtAQAA72Ax\nrjxBCgAAAABQbPyXMQAAAACYgOIKAAAAAExAcQUAAAAAJqC4AgAAAAATUFwBAAAAgAkorgAAAADA\nBBRXAAAAAGCC/wPyfhtxSE2pNAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f12c97ab908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.plot_posterior(trace, varnames=['group1_mean','group2_mean', 'group1_std', 'group2_std', 'ν_minus_one'],\n",
    "                  color='#87ceeb');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looking at the group differences, we can conclude that there are meaningful differences between the two groups for all three measures. For these comparisons, it is useful to use zero as a reference value (`ref_val`); providing this reference value yields cumulative probabilities for the posterior distribution on either side of the value. Thus, for the difference in means, 99.4% of the posterior probability is greater than zero, which suggests the group means are credibly different. The effect size and differences in standard deviation are similarly positive.\n",
    "\n",
    "These estimates suggest that the \"smart drug\" increased both the expected scores, but also the  variability in scores across the sample. So, this does not rule out the possibility that some recipients may be adversely affected by the drug at the same time others benefit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA1gAAAFgCAYAAACmKdhBAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAAOAkFFgAAAAA4yf8DyULHQ+rH5SAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f12d16b9b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.plot_posterior(trace, varnames=['difference of means','difference of stds', 'effect size'],\n",
    "                  ref_val=0,\n",
    "                  color='#87ceeb');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When `forestplot` is called on a trace with more than one chain, it also plots the potential scale reduction parameter, which is used to reveal evidence for lack of convergence; values near one, as we have here, suggest that the model has converged."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZ4AAAEfCAYAAABxkKByAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAGAUwQMAMIrgAQAY9f+uxJDtGKAk5gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f12b6db11d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.forestplot(trace, varnames=['group1_mean',\n",
    "                               'group2_mean']);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZwAAAEfCAYAAAB1ZXBPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nWHCIiMggWHCIiMgg/h/T2AZ5sHPGJwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f12b6b7a710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.forestplot(trace, varnames=['group1_std',\n",
    "                               'group2_std',\n",
    "                               'ν_minus_one']);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>mc_error</th>\n",
       "      <th>hpd_2.5</th>\n",
       "      <th>hpd_97.5</th>\n",
       "      <th>n_eff</th>\n",
       "      <th>Rhat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>difference of means</th>\n",
       "      <td>1.003488</td>\n",
       "      <td>0.464556</td>\n",
       "      <td>0.008673</td>\n",
       "      <td>0.110008</td>\n",
       "      <td>1.929636</td>\n",
       "      <td>2618.006985</td>\n",
       "      <td>0.999933</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>difference of stds</th>\n",
       "      <td>0.944355</td>\n",
       "      <td>0.450525</td>\n",
       "      <td>0.006941</td>\n",
       "      <td>0.152468</td>\n",
       "      <td>1.885434</td>\n",
       "      <td>3567.953258</td>\n",
       "      <td>0.999944</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>effect size</th>\n",
       "      <td>0.595406</td>\n",
       "      <td>0.289738</td>\n",
       "      <td>0.005166</td>\n",
       "      <td>0.040975</td>\n",
       "      <td>1.175411</td>\n",
       "      <td>2756.596339</td>\n",
       "      <td>0.999857</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                         mean        sd  mc_error   hpd_2.5  hpd_97.5  \\\n",
       "difference of means  1.003488  0.464556  0.008673  0.110008  1.929636   \n",
       "difference of stds   0.944355  0.450525  0.006941  0.152468  1.885434   \n",
       "effect size          0.595406  0.289738  0.005166  0.040975  1.175411   \n",
       "\n",
       "                           n_eff      Rhat  \n",
       "difference of means  2618.006985  0.999933  \n",
       "difference of stds   3567.953258  0.999944  \n",
       "effect size          2756.596339  0.999857  "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pm.summary(trace,varnames=['difference of means', 'difference of stds', 'effect size'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "1.\tGoodman SN. Toward evidence-based medical statistics. 1: The P value fallacy. Annals of Internal Medicine. 1999;130(12):995-1004. doi:10.7326/0003-4819-130-12-199906150-00008.\n",
    "2.\tJohnson D. The insignificance of statistical significance testing. Journal of Wildlife Management. 1999;63(3):763-772.\n",
    "3.\tKruschke JK. Bayesian estimation supersedes the t test. J Exp Psychol Gen. 2013;142(2):573-603. doi:10.1037/a0029146."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The original pymc2 implementation was written by Andrew Straw and can be found here: https://github.com/strawlab/best\n",
    "\n",
    "Ported to PyMC3 by [Thomas Wiecki](https://twitter.com/twiecki) (c) 2015, updated by Chris Fonnesbeck."
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  },
  "latex_envs": {
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 0
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
