bayesian_ab_testing.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b48cad3d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running on PyMC3 v3.11.2\n"
     ]
    }
   ],
   "source": [
    "from dataclasses import dataclass\n",
    "from typing import Dict, List, Union\n",
    "\n",
    "import arviz as az\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import pymc3 as pm\n",
    "import pymc3.math as pmm\n",
    "\n",
    "from scipy.stats import bernoulli, expon\n",
    "\n",
    "print(f\"Running on PyMC3 v{pm.__version__}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "30cc5507",
   "metadata": {},
   "outputs": [],
   "source": [
    "RANDOM_SEED = 4000\n",
    "rng = np.random.default_rng(RANDOM_SEED)\n",
    "\n",
    "%config InlineBackend.figure_format = 'retina'\n",
    "az.style.use(\"arviz-darkgrid\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "74f9d767",
   "metadata": {},
   "source": [
    "This notebook demonstrates how to implement a Bayesian analysis of an A/B test. We implement the models discussed in VWO's [Bayesian A/B Testing Whitepaper](https://vwo.com/downloads/VWO_SmartStats_technical_whitepaper.pdf), and discuss the effect of different prior choices for these models. This notebook does _not_ discuss other related topics like how to choose a prior, early stopping, and power analysis.\n",
    "\n",
    "#### What is A/B testing?\n",
    "\n",
    "From https://vwo.com/ab-testing/:\n",
    "\n",
    "> A/B testing (also known as split testing) is a process of showing two variants of the same web page to different segments of website visitors at the same time and comparing which variant drives more conversions.\n",
    "\n",
    "Specifically, A/B tests are often used in the software industry to determine whether a new feature or changes to an existing feature should be released to users, and the impact of the change on core product metrics (\"conversions\"). Furthermore:\n",
    "\n",
    "* We can test more than two variants at the same time. We'll be dealing with how to analyse these tests in this notebook as well.\n",
    "* Exactly what \"conversions\" means can vary between tests, but two classes of conversions we'll focus on are:\n",
    "  * Bernoulli conversions - a flag for whether the visitor did the target action or not (e.g. completed at least one purchase).\n",
    "  * Value conversions - a real value per visitor (e.g. the dollar revenue, which could also be 0).\n",
    " \n",
    "If you've studied [controlled experiments](https://www.khanacademy.org/science/high-school-biology/hs-biology-foundations/hs-biology-and-the-scientific-method/a/experiments-and-observations) in the context of biology, psychology, and other sciences before, A/B testing will sound a lot like a controlled experiment - and that's because it is! The concept of a control group and treatment groups, and the principles of experimental design, are the building blocks of A/B testing. The main difference is the context in which the experiment is run: A/B tests are typically run by online software companies, where the subjects are visitors to the website / app, the outcomes of interest are behaviours that can be tracked like signing up, purchasing a product, and returning to the website.\n",
    "\n",
    "A/B tests are typically analysed with traditional hypothesis tests (see [t-test](https://en.wikipedia.org/wiki/Student%27s_t-test)), but another method is to use Bayesian statistics. This allows us to incorporate prior distributions and produce a range of outcomes to the questions \"is there a winning variant?\" and \"by how much?\"."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9592100b",
   "metadata": {},
   "source": [
    "### Bernoulli Conversions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "448ef06b",
   "metadata": {},
   "source": [
    "Let's first deal with a simple two-variant A/B test, where the metric of interest is the proportion of users performing an action (e.g. purchase at least one item), a bernoulli conversion. Our variants are called A and B, where A refers to the existing landing page and B refers to the new page we want to test. The outcome that we want to perform statistical inference on is whether B is \"better\" than A, which is depends on the underlying \"true\" conversion rates for each variant. We can formulate this as follows:\n",
    "\n",
    "Let $\\theta_A, \\theta_B$ be the true conversion rates for variants A and B respectively. Then the outcome of whether a visitor converts in variant A is the random variable $\\mathrm{Bernoulli}(\\theta_A)$, and $\\mathrm{Bernoulli}(\\theta_B)$ for variant B. If we assume that visitors' behaviour on the landing page is independent of other visitors (a fair assumption), then the total conversions $y$ for a variant has the Binomial distribution:\n",
    "\n",
    "$$y \\sim \\sum^N\\mathrm{Bernoulli}(\\theta) = \\mathrm{Binomial}(N, \\theta)$$\n",
    "\n",
    "Under a Bayesian framework, we assume the true conversion rates $\\theta_A, \\theta_B$ cannot be known, and instead they each follow a Beta distribution. The underlying rates are assumed to be independent (we would split traffic between each variant randomly, so one variant would not affect the other): \n",
    "\n",
    "$$\\theta_A \\sim \\theta_B \\sim \\mathrm{Beta}(\\alpha, \\beta)$$\n",
    "\n",
    "The observed data for the duration of the A/B test (the likelihoood distribution) is: the number of visitors landing on the page `N`, and the number of visitors purchasing at least one item `y`:\n",
    "\n",
    "$$y_A \\sim \\mathrm{Binomial}(n = N_A, p = \\theta_A), y_B \\sim \\mathrm{Binomial}(n = N_B, p = \\theta_B)$$\n",
    "\n",
    "With this, we can sample from the joint posterior of $\\theta_A, \\theta_B$. \n",
    "\n",
    "You may have noticed that the Beta distribution is the conjugate prior for the Binomial, so we don't need MCMC sampling to estimate the posterior (the exact solution can be found in the VWO paper). We'll still demonstrate how sampling can be done with PyMC3 though, and doing this makes it easier to extend the model with different priors, dependency assumptions, etc.\n",
    "\n",
    "Finally, remember that our outcome of interest is whether B is better than A. A common measure in practice for whether B is better than is the _relative uplift in conversion rates_, i.e. the percentage difference of $\\theta_B$ over $\\theta_A$:\n",
    "\n",
    "$$\\mathrm{reluplift}_B = \\theta_B / \\theta_A - 1$$\n",
    "\n",
    "We'll implement this model setup in PyMC3 below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "a5376bb4",
   "metadata": {},
   "outputs": [],
   "source": [
    "@dataclass\n",
    "class BetaPrior:\n",
    "    alpha: float\n",
    "    beta: float"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a0c80bf2",
   "metadata": {},
   "outputs": [],
   "source": [
    "@dataclass\n",
    "class BinomialData:\n",
    "    trials: int\n",
    "    successes: int"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "b625c349",
   "metadata": {},
   "outputs": [],
   "source": [
    "class ConversionModelTwoVariant:\n",
    "    def __init__(self, priors: BetaPrior):\n",
    "        self.priors = priors\n",
    "\n",
    "    def create_model(self, data: List[BinomialData]) -> pm.Model:\n",
    "        trials = [d.trials for d in data]\n",
    "        successes = [d.successes for d in data]\n",
    "        with pm.Model() as model:\n",
    "            p = pm.Beta(\"p\", alpha=self.priors.alpha, beta=self.priors.beta, shape=2)\n",
    "            obs = pm.Binomial(\"y\", n=trials, p=p, shape=2, observed=successes)\n",
    "            reluplift = pm.Deterministic(\"reluplift_b\", p[1] / p[0] - 1)\n",
    "        return model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0e7ba4f2",
   "metadata": {},
   "source": [
    "Now that we've defined a class that can take a prior and our synthetic data as inputs, our first step is to choose an appropriate prior. There are a few things to consider when doing this in practice, but for the purpose of this notebook we'll focus on the following:\n",
    "\n",
    "* We assume that the same Beta prior is set for each variant.\n",
    "* An _uninformative_ or _weakly informative_ prior occurs when we set low values for `alpha` and `beta`. For example, `alpha = 1, beta = 1` leads to a uniform distribution as a prior. If we were considering one distribution in isolation, setting this prior is a statement that we don't know anything about the value of the parameter, nor our confidence around it. In the context of A/B testing however, we're interested in comparing the _relative uplift_ of one variant over another. With a weakly informative Beta prior, this relative uplift distribution is very wide, so we're implicitly saying that the variants could be very different to each other.\n",
    "* A _strong_ prior occurs when we set high values for `alpha` and `beta`. Contrary to the above, a strong prior would imply that the relative uplift distribution is thin, i.e. our prior belief is that the variants are not very different from each other.\n",
    "\n",
    "We illustrate these points with prior predictive checks."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc675d9b",
   "metadata": {},
   "source": [
    "#### Prior predictive checks"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8e1f6ca4",
   "metadata": {},
   "source": [
    "Note that we can pass in arbitrary values for the observed data in these prior predictive checks. PyMC3 will not use that data when sampling from the prior predictive distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "4a103373",
   "metadata": {},
   "outputs": [],
   "source": [
    "weak_prior = ConversionModelTwoVariant(BetaPrior(alpha=100, beta=100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "1d8702af",
   "metadata": {},
   "outputs": [],
   "source": [
    "strong_prior = ConversionModelTwoVariant(BetaPrior(alpha=10000, beta=10000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "9e1e0769",
   "metadata": {},
   "outputs": [],
   "source": [
    "with weak_prior.create_model(data=[BinomialData(1, 1), BinomialData(1, 1)]):\n",
    "    weak_prior_predictive = pm.sample_prior_predictive(samples=10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "4df134b8",
   "metadata": {},
   "outputs": [],
   "source": [
    "with strong_prior.create_model(data=[BinomialData(1, 1), BinomialData(1, 1)]):\n",
    "    strong_prior_predictive = pm.sample_prior_predictive(samples=10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "a3d30bb9",
   "metadata": {},
   "outputs": [
    {
     "data": {
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     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
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H+/fv19SpU7Vr1y5dvXpVZcqUUevWrTV69OhcnTA5c+aM/vjjD4WEhOjChQtKTU2Vv7+/mjdvrqFDh2YZ7sfqxuPXW2+9ZTrG2b4XpcwxpoODg7V9+3aFhobqypUrkjKvrmzcuLH69++vdu3a5ecluGU4a19Zs2aNcbtfv3522/Dy8lK3bt00e/ZsnThxQqdPn1b16tXtrvvII48oNDRUq1evVnJysjw9PfP61ADchgiPAZjY/tjL6w9JLy8vde7cWUFBQVq7dq0SExMdjgloPaPu7u6e5Qt2QkKCnnnmGe3cuTPL+qmpqYqPj9eZM2e0detWHT58WN9++22e+pgfQUFBkqRWrVoZYW2vXr30/fffa+PGjYqOjr5ps2LbVrxmV/0aEhKil19+WTExMVnuj4yM1Lp167Ru3Tq1b99eX3/9dYGqcIrK22+/rXnz5mW57/Tp0/rpp5+0cOFCTZ069a6rCrOtbLH+2LjR6tWr9frrrxtjd+dHeHi4nn76adNVCVeuXNHGjRu1ceNGzZ49W5MmTZKfn5/Dtvbu3asxY8YoOjo63/3JC+v7xTputT1ff/21MaZpdoKCgvTBBx+YXkfrGNQrVqzQY489pg8//NBuxVFaWppeffXVLBNwSplXExw/flxBQUGaMmVKbp9WtsLDw/Xiiy/qyJEjpmXWCVKXLFlSKGF9586dVbx4cV2/fl1LlixxGB6npqZq5cqVkqT27dubwtLk5GS99dZbWrp0qemx1gmDZs2apa+++kodO3Z06vPIL+vnaKVKlbJdJzY2VmPHjtXWrVuz3J+SkqJDhw4ZE6ROmjSpwGPrT5w40QhubcXFxeno0aM6evSoZs6cqS+//FJdunQp0LZs9/ns3mthYWEaOXKk6aRcXiQnJ+vVV181VXfGxMRo79692rt3r6ZPn66ffvpJ9erVc9hWdHR0tu8Vq3379un69euSpMaNGztsr1+/fnaf25UrV7Rp0yZt2rRJs2bN0k8//ZTtCeDcunbtmsaOHatDhw5luX///v3av3+/li9frh9//DHHz/pdu3bphRdeyHI8Tk5ONvo7btw4jRo1yu5jb+bzLSrW4SqkzGHesuPv76/AwECFhYVp9+7dDttp3rx5tu3YLtu9e/dNCY///PNPffDBB0pLSzPuu3TpkubPn68lS5boiy++cDhc2uTJk/X1119nmZBNyvwsCg8P18KFC/Xcc8/pn//8Z4H6ee7cOXXu3NnusgsXLujChQtavny5evfurQkTJuS78reoOWtfsbZTvXp1h++/Fi1aaPbs2UY72YXH1uNfYmKidu7cmePJYQB3htvzSAqg0Jw8edIYhqFJkyYqV65cntvo1auXgoKClJiYqDVr1qhXr15210tLSzPCk7Zt22YZF/H77783guOHH35YvXr1UqVKleTp6amoqCgdOXJE69aty3Pf8uPQoUMKDQ2VpCzPpXfv3vr++++VmpqqpUuX6sknn7wp/bFWvkj2w/1du3bp6aefVmpqqsqVK6cnn3xSdevWVfny5RUREaFly5YpKChIGzZs0Jtvvum02aBvlhkzZujAgQNq1KiRRowYoWrVqikqKkoLFizQ8uXLFRERodGjR2vx4sXy8fFxyjYnT56s1NRUzZgxQzNnzpSUdfI6SSpTpoxGjhypb775xqgEc3Tpn7NZ91FJKl++vGn5hQsX9Prrr6t48eJ67rnn1KxZM7m5uenAgQO5nvQpISFBI0aMMC5/7Ny5swYMGKDy5csrPDxcf/zxh7Zv365du3ZpzJgx+uOPP7KteEtISNBLL72k5ORkjRkzRm3atFHx4sUVGhpaKOHC1atXjcoke6+PlDkpZmhoqGrXrq0RI0aoVq1aSk5OzhIoLVu2TOPGjZPFYlHVqlX15JNPqmbNmipTpozOnz+vP//8Uxs2bNCff/4pHx8fU/WUJH3++efGsa969eoaPXq06tSpo/j4eC1fvlxz584t8GSlV65c0ZAhQxQRESFJatmypfr166caNWpIyvwxv3XrViO0lTKHHFi8eLHWrFmjb775RlLmvn/j65VdlbMtHx8fdezYUcuWLdOqVas0fvz4bKuTNm7caJzouvHzwmKxaOzYscbn0sMPP6xHH31UVatWlaurq/bv368pU6bowoULGjt2rGbOnGm3su1mWrBggVHhba9yW8oMiP/xj3/o0KFDcnNzU8+ePdW+fXtVqVJFqamp2rlzp6ZMmaKoqCg988wzRrW+lPm+a9iwocPjkaQsldhpaWny9/dXly5d1KRJE1WtWlWenp66ePGi9uzZoxkzZigxMVGvvvqqFixYUKCTbzkdiyRp7NixioiI0LBhw9SxY0eVKlVKZ86cydMJ6zfeeMMIjuvWrat//OMfqlmzpmJjY7V06VItWLBAERERGjFihIKCghxWpr/zzjsKDQ1V37591b17d5UrV04XL17McoLW+p3ExcVFDRs2dNi39PR0NW7cWB06dFD9+vVVtmxZpaamKjw8XEFBQfrrr790+PBh/etf/9L06dNz/Zztef/993Xo0CF1795dffv2VdmyZRUWFqapU6fqwIED2rFjh8aNG6eJEydm20ZERIReeOEFubq66tVXX9UDDzwgDw8P7d69WxMnTtS1a9f03//+V+3atbM7UezNfL5Fxfa7l/U4mp0aNWooLCxMFy9eNBVRWMfMLlmypMPPuvLly8vHx0fx8fFZtl1Yjhw5oiVLlqhMmTJ69tln1ahRIyUnJ2vDhg2aNm2aUlJS9Prrr6tKlSp2j7G//PKLvvzyS0mZlcRDhgxRYGCgSpYsqdOnT+uPP/7Qnj17NGnSJJUuXTrLVS6LFy9WRESEcXLi5ZdfNh07rVdTSZknyD08PNS2bVu1adNG9957r3x9fRUbG6vTp09rxowZxonYqlWrauzYsYXxkhU6Z+wrCQkJunjxoqTc7bdWjva5Ro0aGbe3b99OeAzcJQiPgbtQVFRUlh93FotFcXFx2rNnj6ZNm6br16+rZMmSdkOP3GjdurXKli2rqKgoLVmyJNvweMuWLcbYrDeus3z5ckmZl0bZqyxu166dnn32WVNlbWFYuHChpMyqatuKrGrVqqlx48bat2+fFi5ceFPC41WrViksLExSZhX0jRV6qampev3115WamqqHHnpI3333XZZLKxs0aKCHH35YzZs313vvvadVq1Zp8+bNt9UXvwMHDqh9+/aaNGlSlmqS9u3bq1atWvr222914cIFTZo0ye6YhPlhrb6w/fFib9LJcuXKGcMNeHh42F2nMKxfv17Hjx+XlDk8g71qx/DwcJUvX16zZ8/OEtDkVEFn6/vvvzeC4+eee04vv/yysaxhw4Z65JFH9Prrr2vx4sXas2ePZs+erSeeeMJuWzExMfL29tbMmTNVt25d437bHyXO9PPPPxuzn2dXNRYaGqpWrVrpp59+ynJ5tbWq5+rVq3r//fdlsVg0YMAAffTRR1n2wQYNGqhr165G9fJvv/2mwYMHZ/lBduzYMf3+++/G+tOnT89SEdiqVSs1bdrUGPIhv8aPH28Ex6+99pqefvrpLMsbNWqk7t2764033jCqzKwTDh48eNBYLzAwMFdhsT29evXSsmXLFB8fr3Xr1qlbt25211uyZImkzMDZOou81dy5c7V+/Xp5eHho0qRJpsuQmzRpoj59+mjo0KE6fvy4PvvsMyNQLUzh4eFZrjbJyMgwqu9nzJghSapVq5ZGjhxp9/ETJ07UoUOHVKpUKU2ZMsUURjZr1ky9evXS4MGDFRkZqf/+97/GpfClSpVSqVKlcjwe2Ro4cKBefPFF09UqDRo0UOfOnTVs2DANGjRIly9f1g8//GCEQHl1+fJlI8h2cXHJtlru+PHj+vnnn42xOiXlGMjaWr9+vfE9wd57tm3btrr//vv13nvvKSYmRhMmTDBOiNhz7NgxffLJJxo4cKBxX4MGDbKss2fPHkmZx9iSJUs67N+0adPsTqratGlT9e7dW/PmzdPbb7+t7du3KyQkRK1atcrpKWfrwIED+te//mWMtStlvpbdunXTs88+q02bNmn16tXasGFDtkNPhIWFKSAgQDNnzswSsjdq1EgNGzbUk08+qbS0NM2ePVvvvvtuoTxf65BGBWEdnqkwXLp0ybid0xA51s9gi8WiS5cuZfkMsE68W7FixRy3WalSJR0/fjzLtgvL0aNHFRAQoNmzZ2cJKps3b662bdtq1KhRSk1N1Ycffmga6/bEiRPG++vFF1/Uiy++mGVYtIYNG6pHjx564403FBQUpK+//lp9+vQxvsPWrl07S8BeoUIFh8c0f39/rV271u7JqVatWmnIkCF6++23NX/+fE2ZMkX/+Mc/7L5n7Q1Jllc3DqfhTM7YV2z/zqkd2+WO9jlfX19jqLMbr3gAcOdiwjzgLjRz5kz16tXL+Ne7d28NHTpU//nPfxQVFaXHH39cc+fOzfdlsu7u7saEOZs3b872knTrD0xvb29ThYG1QrBZs2YOt5XTZfEFlZaWZlwq3alTJ9Nln3369JGU+eOtsCpDUlJSdPLkSf34449GGOrl5WW3MnHp0qU6f/68PD099cUXX2Q7Jt+gQYOMkG7+/PmF0u/CUqxYMX388cd2L0N87rnnjB8c8+bNy/OY3beTjIwMXbhwQb/++muWEHf06NHZPubVV1/N95imKSkpxg/GWrVq2f2x5OLiovHjxxvvyz/++MNhm6NHj84SHDtbSkqKQkND9f777xsTHbm7u2vEiBF213d1ddUnn3yS7bicM2fOVFxcnCpUqKDx48dneynsSy+9pAoVKigjI8MY+9Vq1qxZxrAiH330kd1Lyfv27VugsRpPnTql1atXS8qsUr0xOLZVokQJu+MLO8NDDz1k7Av2KmOlzKoo23FkbauTLRaLfv75Z0mZY3dn95r4+vrq9ddfl5R5qa31BFthevvtt7N8jvbp00ejRo3StGnTVLx4cb3yyiuaMWNGlitqrBISEoz3xj//+c9sQ9OAgAA9//zzkqSVK1cWaLiZKlWqOJzks2LFikbV39q1a40TLblhsVgUHR2tZcuWaciQIbp27ZqkzImcbOdQsNWvX78swXFeWV8/Dw8PTZgwwe57dtCgQcbY48HBwcbJFHtatmyZJTi2xxqm2Ib22bEXpNoaMGCAMZSG9b2aX3Xq1NEzzzxjut/d3V2ffvqp8f9uPamRnXfffdduKNqsWTPjJKPtZfS2bubzLSoJCQnG7ZyGALH97nXj+9baTm6u+LG2Y7vtwvTGG2/YrXC1fX8cOHDANBHor7/+qtTUVDVs2NAUHFu5urrqvffeU7FixZSYmJjlqpe88vb2zvaqBinzu8gbb7whNzc3JSYmasuWLfneVlFyxr5i+3dO7dguz+nzxnoctBYUALjzUXkMIAvr5Eqenp567bXX8j25Sa9evTR9+nSlpqZq+fLlpurD69evZwk3bgw5/f39deHCBS1btkwDBw7MNgQtbH/99ZdRHd27d2/T8kcffVQTJkxQamqqgoKCCnypuZW9yY+sGjRooHfeecduxag1hGnevLnd0MJWs2bNtH//fu3du7dAfb3Z2rRpk23Vj6urq/r27asvvvhCMTExOnz4cIHHCr2VONovJGnw4MHGBJQ38vDwcDhWYU4OHjxohEL9+vXLdjgKHx8fPfroo5o5c6ZOnDihiIiIbH/k2XtPFcT27dsdvkYeHh76+OOPs61oatq0qcMqW+v7q0OHDg6Pje7u7mrSpIlWrlxpVCtaWX/E1q5d22Gl5YABA7Rx48ZslzuyYcMGI/zLLii/GTw8PNStWzfNmjVLGzdu1LVr10wTAQYHBxvjyN64P5w4cUJnz56VlHkViiO2Fa579+7NMcwqTHFxcZo7d678/Pzsvh937NihuLg4Sbl/XqmpqTp06JDDcS/zIj4+XtHR0bp+/bqxr1g/Z+Pj4xUeHq6qVatm+/gbJ1a80X333acPP/ww2+XZXZGUG2lpadqxY4ekzM8DR+NKDxw4UFu2bFFaWpq2b9+unj175rs/1hPheZ2Q1WKx6MqVK4qPj88yFmyFChV05MgRHT16NE/t3ahfv37ZTn5bsWJFtWnTRuvXr9f27duVnp5u99hdqlQpdejQIdttNGjQQHv37s1VUJTf5/vKK69kW6mfW4X5XTE5Odm47ehEjKQsnw/W49uN7eTUhm07ttsuLL6+vtkOsyNlfiZZr+oICQnJMnSFdRi5nCZiLlWqlHF1y549ezRo0CCn9D01NVVRUVFKSEjIMs66n5+foqKidPToUbvHWuuQZAWRm5NJ+eWMfcW2iKIg++2NrCedrcU+AO58hMfAXcjeJVbXr1/XmTNntGjRIk2bNk3Tpk3TwYMHNXny5Hx9GW/cuLHuuecenT17VosXLzaFx9bJ9CT7P9r69u2rSZMmac+ePerUqZO6deumVq1a6YEHHsgxFHUm6yWUZcuWtTu0Q5kyZdS2bVutW7dOQUFBevnllx1+cS4oDw8PDRgwQA888IDd5dbLzTdt2pRj0Gh1u33xy2k8U9thD0JDQ++o8NgeLy8vNW3aVE8++aTDycICAwMLNCO2dVgMKeehLho3bmz8yDx+/Ljd8Njb29thOOVMpUuX1kMPPaRRo0Y5rHR29J5JT083Qo/Zs2cbk8rkxPb9lZKSojNnzkjK236cV4cPH5aUebzIy7AkhaFXr16aNWuWUlJStHLlSlN1p3XIivLly5sm7bMdPiMvk0VFRkYWoMe5c+MkgxaLRfHx8Tp69KimTZum4OBgffDBBzp9+rRpCCjb55WX6tuCPq/z58/r119/1bp163K8VDs6OjrP7083NzfVrVtXffv21ZAhQxwGFbn9fLLn3LlzSkpKkpTz+8R2/7c9huWnP9ZhsnIbHq9fv14zZ87Ujh07HFaOFnTC0JyOJffdd5/Wr1+vxMREnTt3zu6JlWrVqsnVNfsLUq1BkaPnUdDnW6FChRyHgyhKtp+fqampDj9PbQO74sWLm9pJSkrKVWhpbacgn925Va9ePYcTy9WrV08eHh5KTU3VsWPHjPvPnz9vjPH+1VdfGcPr5KSg3z1TU1M1Z84cLVq0SIcPH3b4ema3z2U3Idytwhn7im0gnFM7jvbbG1mPg9ZjMYA7H+ExAEmZXxLq1KmjcePGKTAwUO+995527dqlH374Id/VtL169dLEiRO1Z88ehYeHZ6noCwoKkpQZylovK7X1/PPP6/Lly5o/f76ioqL0xx9/GJep1qpVS127dtUTTzyRrwn9cuvatWtGNUX37t2z/VLdu3dvrVu3ThcuXNC2bdvUsmXLAm/b9hLva9eu6dixY5o6darOnj2rjz76SElJSXaHJ7B+gc+LnKoL8sM2QM/t5c+5XS+nKg/b5TdjTOybyXa/cHNzU4kSJeTv759tFbCtvFbL3Sg2Nta4ndMJHNv3pe3jnNkfexo2bKgJEyYYf7u7u8vX1zfXlUGO+hQbG5tlBvrcsn1/xcbGGvt5Tn0qyLHN+kPZ19c331ePOMsDDzyggIAAnT9/XkFBQVnC46ioKIWEhEiSevToYQqvrFd95FVhHNNy4uLiopIlS6p58+Zq3ry5Xn31VS1ZskRTp05V+/bts3zOFcXz2rBhg/75z3/m+od+Ttv67LPPjNDSxcVFXl5eKleuXI6Bg1VBhkqxPabk9D6yvQTf0edBbvrj6emp1NTUHKtALRaL3n33XdO4sNkp6P7qjONxTkUC1vemdcgdWzf7+RYV26EqEhISHAa6tu+zG4cKKFGihJKSknI1DI21nZyGyXCGnN5L7u7u8vPzU2RkZJb9qCiOZzExMRo5cmSux9u9GZXbhcEZ+4rt3zm1Y7s8pyEurK+poxMOAO4svNsBmDz22GP66quvFBMTo3nz5hU4PLZYLFq6dKkxmUtMTIw2bdokKftQ1sPDQ5999plGjhypJUuWaOvWrTp48KBSU1N1/PhxHT9+XFOmTNGXX36pzp075//JOrBs2TLjLPz06dNzNQnLokWLnBIe33hZfbNmzdSnTx898cQTOnbsmL7++mu1aNHCVHVlvVyvXbt2xhigRcH2R1Vuv7Rbv7Tm9IW1MCu7b3UFmYAvNwFzbjnj/8CZ/bGyTviWX476ZHsp7MCBA3O8bN8qu+rLu2U/dnFxUc+ePfXjjz9q586dunz5slFduHz5ciOQt3cFim1Q9cMPP2Q7fu6NCvMy4twaPXq0UVU9b968LOGx7b60YMGCXP/4zs2kSfZcvXpVr732mpKSkuTt7a1Ro0apbdu2uueee+Tj42OcYAgJCTGGOcnpZF6VKlVuieORs95HjqpurcqUKaP4+PgcT0r++eefRpBar149PfXUU2rUqJEqVKggLy8v47mPGzfONCZ6fhT1scRZz/fy5cvZhtu55eXlVWhXtNi+/y5fvuwwtL948aKkzP+bG9+3FSpU0JUrV3I1CZ61nfy+9/Miv/uR7XH6hRdeyHZi1BsVZIiRTz/91AiOO3furAEDBqhOnToqW7asPD09jefSoUMHXbx4Mdvj2enTp50ybEVhfeY4Y1+xrebPqZ28TK5nfa8WRiEAgFsT4TEAE1dXV1WrVk0xMTGKjIxUdHR0llnlc6t69epq2LChDh48qCVLlhjh8cqVK40vazmNM3jvvfcak4ElJydr165dWrx4sRYtWqTExES9+uqrCg4OdjhxRn4tXLgwz49ZuXKl3n///UIZd8/Hx0dffPGF+vXrp7S0NH3++eemCcn8/PwUERGh1NTUAv2wLyjbiQxze6m19RLGnCrAcrrU0bYKprAnVLyb2P6/REVFObzc0/b/qLAmY7vZbJ+HxWLJ1/vL9kdWTvtxQS7ptR6vY2NjlZKSUuTVx7169dKPP/6ojIwMLVmyxJiYzRqu1qhRQw0aNDA9zvb9W7JkySI9puVVjRo1jNuhoaFZltl+npYpU6bQg6GVK1ca45VPnDjR7tU+UvZVqbca2/diTu8T28+fgn4elClTRmfPnjVey+zMnTtXUuZQELNmzcq2GttZr3dRH4+d9Xy//vprY6iw/GrRokWuTvTnR82aNY3bp06dMiYAtOfUqVOSpEqVKplOiN977706dOiQ4uLiFBkZaXeCOkmKiIhQfHy8aduFJaf3UlpamnHixHY/sn1fubu7F/pxOj4+XsuXL5eU+dnyn//8J9t1c9rnRo0aleMQPjmxNxSgszhjX/Hx8VGlSpV08eJFY7/Mju3ynPY562vraMx5AHeWnE+zA7gr2V6ebVsllVfWcDg0NNQYL9R66f0999yTp/E4PT091bp1a02YMEHjxo2TlHnZ2/r16/Pdv+ycPXvWmOiqR48e+u9//+vwn7U6OyEhQcHBwU7vj1XdunWNCX927txpmlCrfv36kjLH1LQdu+xmsx0/MjeXFV65ckWXL182PdaeG2f5drS8Vq1aOW7b2Yq6Cqyw2L6W+/btc7ju/v377T7udlasWDHjuezevTtfbXh6ehrjjeZlP84raxCbmpqarwkxnb0P16pVyxhr2hoYnzt3zjjGZncS0Tacye9rXlRsP0NvHO7EWc8rt/9PJ06ckJQZ8mQXHEtZx2K+lVWtWtU4QWt7rLHHmcciayh29uxZu8M3WFnHVu7YsWO2QarFYsn1Jfc5yelYYf1/Layq3Jv9fIuK7VwT27dvz3a9yMhIhYWFScqchNVRO9aJH+2xXWavHWc7evSow6GZjh49ahR+2AbEVatWVcmSJSXdnONZWFiY0Y/u3btnu97JkydzNdzDrcxZ+4q1ndOnTzss6LDdrx3tcxkZGcbkmffee2+26wG4sxAeAzBJSkrSyZMnJWWOhZyfqmOrHj16GJcsLl68WJcuXdLOnTslFWy2dduhIQo62Yw9tlXHI0eOVI8ePRz+Gz16tFF94YzLUB0ZM2aMcYnt//73vyzLrBOmxcXFaf78+YXaD0fq1atnvB7BwcE5Dl1hO5Zvq1atHK67efNmRURE2F2WkZFhVC75+vrarWYsbNYqz6IM7wtDw4YNjcrZhQsXZhue2FYF3XvvvYVyVUBRsb6/Tp06pb/++itfbVj379DQUGNiO3vmzZuXr/YlqX379sYP8WnTpuX58bbDzjhrP7Ye7w8fPqyTJ08aIbLtshs1aNDAqMqdM2fObTVupW0Qe2NlVuvWrY3w87fffsv1eO83sq0od/T/ZA2EkpOTs33fJiUlFfpnl7O4u7urefPmkjI/Dxxdim0dTsHd3V0tWrQo0HatAUxiYqLxHcke6wl3R8HVmjVrnDax46JFi7Ldhy5fvmwME9aiRYtCGS7IWc/33//+t44dO1agf4VVdSxlXk1nrcZcsWJFtuOH21ZP2xtWrWPHjsZ3OEfHeet3OFdXV4eT4TpLTEyMMc+HPbZ9tf2e5ubmpvbt20vKfD86em84ktvPHduCFkdjuM+aNSvHba5du7bA+1xhVR1LzttXOnXqZNzOrro/KSlJK1askJT53c3R1QwnTpww3u9FPSkvgJuH8BiAyXfffWdMZNG2bdsC/djw9/c3gt6lS5dq8eLFxo+c7AKDmJgYrV271uEP6s2bNxu3bSfik6Tw8HDVqVNHderU0bBhw/LcZ4vFYkzoFxAQoIYNG+b4GHd3d+NHQkhISLbhpjPUrFlTXbp0kZRZ5bF161ZjWb9+/Yyg4vPPP3dYqSBlVi87qqDJLw8PDw0ePFhSZhXOZ599lu3/57FjxzRp0iRJmWPW9u/f32HbKSkpev/99+1WxP/000/GJeIDBgwoksv1rZcVRkVFGZcR3gmKFSumxx57TFJm8Gn9P7NlsVj08ccfGyd0hg4delP7WNiGDx9uXIL81ltvGRV32Vm/fr1xxYXV448/bgS77733nt3AJSgoSBs2bMh3P6tXr24cI1avXq1ffvkl23UTExNNl/baXhprrS4qqJ49exrPOygoSEuXLpUk3X///dlWQ7q6uhrDHZ07d07jxo1zGCrEx8fr999/t7ts2LBhxudCeHh4QZ5KjlJSUvR///d/xt/WYMWqVKlSxntjz549+uyzzxxWsl65csUYGsCW7YmZs2fPZvt4a7V7UlKScWLHVnp6ut59991C/dxyNuvrl5qaqnfeecfuuKV//vmnEZx26dKlwCeymjVrZtx2VPFcrVo1SdK6devsjo989uxZffjhhwXqi60jR47YfY+npaXp3XffNV6bIUOGOG2btm728y1KI0eOlJT5PfXLL780LT979qx+/PFHSZmvi/U4bMvf39/4/rtp0yYjsLO1fPlyY9/t06dPtsMVdOzY0TiuOcOECRPsDl+xfft2zZkzR1LmSb0b59t45pln5ObmpoyMDI0dO9bhCZ309HQFBQWZ1vHz8zPmCHB0PLvnnnuMz5IFCxbY/W65du1a07ButyNn7StdunQxPmd//PFHu6/vF198YXwXsA4tlR3b41+bNm1y+WwA3O4Y8xi4C0VFRZnGYExOTtaZM2e0cOFCo6LO09NTY8eOLfD2evXqpc2bN+vixYv66aefJGVWMWZ3Vjs+Pl7PPfecAgIC1LVrVzVq1EgBAQFyc3NTZGSk1q1bZ/yQrlChgjp06FDgPtratWuXEZg88sgjuX5c165d9eeffxpfjEePHu3UftkaM2aMVq5cKSmz+tga0BcrVkzffPONhg0bpsTERD311FPq3r27OnfurCpVqigjI0ORkZE6dOiQgoODFRoaqvfee6/AFVnZ9TE4OFinTp3SrFmzdPjwYT322GOqXbu2PD09FRkZqc2bN2vOnDlG9cgHH3yQ4+QbDRs21Lp16zRkyBCNGDFC1apVU1RUlBYuXGgEUhUrVtTzzz/v9OeUG9ZL/TIyMvTBBx9o2LBhWar3rT+0b0cvvPCCgoODde7cOX333XcKDQ1V//795e/vr/DwcP3+++/GyYj777/fOIFwpyhXrpw+//xzjR07VpGRkRowYID69eundu3aqWLFikpLS9OlS5e0f/9+rVy5UufOndMPP/xgDNkgZQ49M3ToUP3+++86ePCgBgwYoKefflq1a9dWXFycVqxYoTlz5hjjxefXBx98oL179yoiIkJffvml/vrrL/Xr1081atSQi4uLzp8/r23btmnZsmX69ttv9eCDDxqPrVevnjw9PZWcnKz/+7//k7u7uypXrmxUQFWoUCHby9OzU7FiRTVv3lzbt2/XjBkzjHFjc7oCZciQIdqyZYuCg4O1YsUKHT58WIMHD1ajRo1UsmRJxcfH69SpU9q+fbvWrl2rYsWK6cknn8zjq5V34eHhpqty4uPjdeTIEc2cOdM4sVCtWjW774N//vOf2rFjh/bt26fffvtN27dv16BBg1S3bl15e3srNjZWJ06c0JYtW7Rx40bVrl1bAwcOzNLG/fffb9yeMGGCxowZI39/fyNYCQgIkLu7ux599FH997//VUpKit566y0dOXJEbdq0kY+Pj06cOKHp06fr0KFDatq06W0zPEiHDh3UrVs3rVixQps2bdLgwYM1YsQI1ahRQ9euXdPSpUuNSj0/Pz+99dZbBd5mlSpVVKdOHR07dkwhISEaMGCA3fX69u2rL774QhERERo8eLDx/k5OTtbWrVs1bdo0paSkqEGDBk4ZyqFhw4b6z3/+o6NHj6pPnz4qW7aszpw5oylTphghz8MPP6yHH364wNuy52Y/3/xasWJFlpN1u3btsntbyjzWt2vXztRGv379NG/ePO3evVt//PGHrly5ooEDB8rX11f79+/XpEmTFB8fL1dXV73zzjvZTob5yiuv6K+//tLVq1f16quv6uDBg8Z32fXr12vKlCmSMsfZts77Udjq1q2rkydPqn///nr22Wd13333KSUlRRs3btTUqVOVlpYmd3d3ffDBB6bH1qlTR+PGjdOECRN04sQJ9ezZU4MGDVLLli1Vrlw5JScn6/z589q7d69WrFihyMhILV68OMt47+7u7rrvvvu0e/duzZs3T/Xr11e9evWM19DX11d+fn4qXbq02rdvr/Xr1+uvv/7SyJEjNWTIEFWuXFlRUVFatWqVFixYoKpVq+ratWu6evXqTXn9bpSQkGB8T7c6c+aMcXvlypVZPkPq1atndxxtZ+wrHh4eeu+99zRmzBjFx8dryJAheu6559SoUSPFxsZq7ty5Rl8feOAB9enTx+FzCwkJkZS5zxTWBJUAbj2Ex8BdaObMmZo5c6bDdcqUKaMvv/zSKdUMXbp00fjx43X9+vVcBwaSdP78eeNLkT3+/v6aNGmSSpQoUeA+2rIdsiIv4XHr1q1VqlQpXbt2TYsWLSrU8Lh+/fpq3769NmzYoK1bt2rv3r1q0qSJJKlJkyaaPn26Xn75ZV28eFGLFy/OMizEjXx8fAqlj97e3po2bZrGjh2rPXv2aP/+/dlWa3l6euq9995T3759c2x36NCh2rFjh+bPn2+MNW3L399fkydPNsbgu9latmypJk2aaO/evVqyZEmWy/OlzErr25WPj4+mTp2qp59+WqdOndLKlStNP46kzAD9f//7X6FcIl3UunbtqkmTJumtt95STEyMZs2ale3lsa6urnYnz3zzzTcVERGhVatW6dSpU6Zgq0qVKvrmm2/sXvKcW+XKldOMGTP0/PPPKzQ0VFu3bs1ylYIjPj4+GjZsmH755RcdOnTIqLaz+u2337KEzbnVu3dvbd++3fgcsAabjri4uOjrr7/Wp59+qlmzZuns2bN2K/6sypQpY/d+69U0Hh4eTjnmvf322zmuU7duXU2cONFu0F6sWDH9+uuveuutt7Rq1SodPXpUH330UbZt2etztWrV9OijjxqVZ9bqM6s1a9aoSpUqqlixosaPH693331XycnJ+vnnn/Xzzz9nWbd79+4aNGiQRowYkePzulV88cUXSk9PV3BwsA4dOqTXX3/dtE758uX1008/qUKFCk7Z5qBBg/Txxx9rzZo1SkpKsvv+Hj58uLZs2aJNmzYpLCxM77zzTpblxYsX1+eff64NGzY4JUz9+OOP9c4779j9vJEyj8eOJhUrqJv9fPPriy++yHZytD///NMY4kTKHOLDXnjs5uamiRMn6plnntGBAwfsfgYWK1ZM77//vumKA1uVKlXSDz/8oBdeeEGRkZF235P+/v6aOHGiwwk1rcc1Z0wOXK9ePT355JMaP3683WORh4eHPv/882yHKRgxYoS8vb312WefKS4uTpMnT9bkyZPtruvh4ZFlmAqrZ599VmPGjFFMTIxeffXVLMtsJ6YbP368nnjiCV24cEFbtmzRli1bsqxbuXJl4/+pqERHRzs8afXFF19k+fvFF1+0Gx47a19p3769PvzwQ3300Ue6cuWKPv74Y9M6jRo10vfff+/wu1tSUpLWrl0rKfMzHcDdg/AYgKTML3J+fn6699571b59e/Xv399ps3L7+Pjo4YcfNi6XdXNzU48ePbJdPyAgQHPnztXGjRu1Z88enT9/XlFRUUpMTFTJkiV177336uGHH9bgwYOdHnwmJycbl4VVqFAhT2N5eXh46OGHH9aiRYuM8UytE9gVhjFjxhiXtk+aNMmo6pYyA+RVq1Zp/vz5WrdunQ4fPqzo6Gi5urqqTJkyqlmzppo3b66uXbuqRo0ahdbH8uXLa+bMmVq3bp2WL1+uvXv36sqVK0pNTVXJkiVVvXp1tW7dWoMHD872skx7JkyYoDZt2mj27NkKDQ1VYmKiKleurM6dO+uZZ54plBnlc8vV1VWTJ0/WL7/8onXr1uns2bNKSkrK97imt5oqVapo0aJFmjt3rlasWKHQ0FAlJCTI19dX9erVU69evdSrVy+jSvVO1LFjR61Zs0Zz5szRhg0bdOLECcXGxsrNzU3lypVTrVq11LJlSz3yyCN2ZyL38PDQd999p0WLFmnOnDk6duyY0tLSVLlyZXXp0kUjR450yj5ctWpVLVy4UEFBQVqxYoUOHTqkmJgYubm5qWLFimrSpIm6du2a5XJ8q9dee02BgYFauHChTpw4obi4uAJNnip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SpVWpUiWdO3dOS5YsUefOnXO8DVJyCFa9enVdvHhRUvItW6VLl7Zb9tatW5o9e7Y2bNig4OBgRUVFqVixYqpXr5569+6tLl263DMTOtj2kLBObLNq1SrNmzdPx48f1+3bt1W+fHl16tRJo0aNUpEiRbK0ntTGuGvfvr0xCYfV3ZO09enTR4sXLzb+f+HCBbsTueXEsBDOzs6qV6+e0caLFy+qZMmSkv434V6TJk00a9YsBQcHa+bMmdq6dauuXLmiO3fuGOPa2vuc7YmLi9P8+fO1evVqnTx5UlFRUSpatKjq1Kmj7t27q0ePHqmOdXf3ZxwWFqYZM2Zo48aNunjxoqKjozM8yWJmVKhQQcWKFVNERISx/1hZ/04vv/yyXnnlFQUEBGjOnDk6cOCArl27prJly5puob969ar++OMPbdmyRaGhoYqOjlbJkiXl6+urgQMHZqi36bJly/TXX3/p2LFjSkhIkLe3tzp37qzhw4enuw1ndFzipKQkrVy5UmvWrDEmtpGkhx56SPXq1VOnTp3UoUMHubm52Z1Y1V7PJNu/T2rj7i5ZskT/+te/JCX/UGzZsmWa72f8+PGaN2+e3NzctG3bNrsTG+7YsUOLFy9WYGCgrl27JhcXF3l7e6tVq1YaPnx4vhqKxNvbW+Hh4Rn6Dl27dq38/Px08OBBXb9+Xe7u7qpYsaLat2+voUOHmj4L27+9lb1jje12kZSUpJ07d2rz5s3at2+fzp49q6ioKHl4eMjb29uYoMh6cTI7GjRoYNypY7uv3b2t3Lp1SzNnzpS/v79CQ0N169atFMcd63E3vcmc1q9fryVLlmj//v26ceOGChUqpMqVK6tDhw4aMmRIqmHh3ftQmTJlNHv2bK1cuVLnzp1TRESEcUyQkse/tB4H0vvOj4yM1Nq1axUQEKCgoCBdunRJ8fHxKlq0qGrVqqXOnTurT58+Wb5ryV7bZ82apeXLlyskJEQWi0XVqlVT7969NWjQoAyPPX3lyhX9+uuvWr9+va5cuSIPDw/Vq1dPw4YNS3MSrJx+v/nB2bNndfr0aUlS165dU50osU+fPsa579q1a02h1vr165WUlCQp+UJTavr27autW7cqKSlJ69ev18CBA1M8v27duhTrtMfDw0Ndu3bVvHnzdOrUKZ09e1ZVqlQxnrdYLEY9VatWTXUYNl9fX1WpUkVnz57VunXrNH78+Fw5f4yLi8vWdp2YmCg/Pz+tXr1aR44cUUREhAoVKqSqVauqc+fOGjx4sCkAvXti0Iycy8XFxWnr1q3aunWrDhw4oJCQEEVHR8vLy0sVK1ZU69atNWTIkHv6LgxHbSv3435kq0uXLjpx4oTWrl2r2NhYubu7p9o2ANlDeAzkA7Y/9jL7Q9LDw0MdO3aUn5+f1q9fr+jo6DTHBLReNXZ1dU1xYnD79m0999xzCgwMTFE+Pj5eUVFROnfunHbs2KGgoCB9++23mWpjVvj5+UmSmjdvboS1PXr00HfffafNmzcrPDw8w7P5Zpdtj9fUer8GBATo9ddfN2ZStrp69ao2bNigDRs2qE2bNvr666+z1Qsnr7z33ntauHBhisfOnj2radOmacmSJfr9998fuF5htrf0WU+o77Z27Vq98847xtjdWREaGqpRo0aZ7kq4du2aNm/erM2bN2vevHmaOnWqihUrlmZd+/fv1+jRoxUeHp7l9mSGdX+xjlttz9dff22MaZoaPz8/ffjhh6bP0ToG9erVq/Xkk0/qo48+snurZUJCgt56660UE3BKyXcTnDx5Un5+fvrtt98y+rZSFRoaqpdffllHjx41PWedIHX58uU5EtZ37NhRBQsW1J07d7R8+fI0w+P4+HitWbNGktSmTRtTWBobG6uxY8dqxYoVptdaJ8WZO3euvvrqK7Vv396h7yOrrN+jDz30UKplIiMj9eqrr2rHjh0pHo+Li9ORI0eMCVKnTp2a7bH1v//++xSBiNWtW7d07NgxHTt2THPmzNEXX3yhTp06ZWtdttt8avtacHCwRowYYboolxmxsbF66623TL3SIiIitH//fu3fv1+zZs3StGnTVLt27TTrCg8PT3VfsTpw4IDu3LkjSWrYsGGa9fXp08fue7t27ZoRMs2dO1fTpk1L9QJwRt28eVOvvvqqjhw5kuLxgwcP6uDBg1q1apV++umndL/r9+zZo5deeinF8Tg2NtZo75gxYzRy5Ei7r83N95tXrLfZS8nDvKWmdOnSqly5soKDg7V3794062ncuHGq9dg+t3fvXlPoZa2nSpUqaX6mTZo00bx584x6bEOv0NBQhYWFpdsWaz1nz57VlStXFBoaqgoVKqRZPruyu11fvHhRL7zwgo4dO5bi8YiICO3du1d79+7VnDlz9NNPP6UaBGbU+PHjU3QesF1XRESEDh48qD/++ENTp07Vo48+mq115RVHbSv3435ky/rdEB0drcDAwHQvnAPIOsJjII+dPn3aGIbB19c3S7c39ejRQ35+foqOjta6devUo0cPu+USEhKM8KRVq1Yprsh/9913RnDcrl079ejRQw899JDc3d11/fp1HT16VBs2bMh027LiyJEjOnHihCSleC89e/bUd999p/j4eK1YsUJPP/10rrTHesVesh/u79mzR6NGjVJ8fLxKlSqlp59+WrVq1VKZMmUUFhamlStXys/PT5s2bdK7776rKVOm5Eq7HWX27Nk6dOiQGjRooOHDh6tSpUq6fv26Fi9erFWrViksLEzPPvusli1bJi8vL4esc/r06YqPj9fs2bM1Z84cSSknr5OkEiVKaMSIEfrmm2+MnmBp3d7maNZtVJLKlCljev7ixYt65513VLBgQb3wwgt67LHH5OLiokOHDmV40qfbt29r+PDhxi1+HTt2VL9+/VSmTBmFhobqzz//1K5du7Rnzx6NHj1af/75Z6o9g27fvq1XXnlFsbGxGj16tFq2bKmCBQvqxIkTORIu3LhxQ9euXZNk//ORkifFPHHihB5++GENHz5cNWrUUGxsbIpAaeXKlRozZowsFosqVKigp59+WtWqVVOJEiV04cIFLViwQJs2bdKCBQvk5eVl6iEqSZ999plx7KtSpYqeffZZ1axZU1FRUVq1apXmz5+f7clKr127psGDBxs/9po1a6Y+ffqoatWqkpJ/CO7YscMIbaXkIQeWLVumdevW6ZtvvpGUvO3f/Xml1svZlpeXl9q3b6+VK1fq77//1oQJE1LtgbN582bjQtfd3xcWi0Wvvvqq8b3Url07Pf7446pQoYKcnZ118OBB/fbbb7p48aJeffVVzZkzJ8VEdnlh8eLFRg/v1MaUjIuL0z//+U8dOXJELi4u6t69u9q0aSMfHx/Fx8crMDBQv/32m65fv67nnnvO6K0vJe939erVS/N4JClFT+yEhASVLl1anTp1kq+vrypUqCB3d3ddunRJ+/bt0+zZsxUdHa233npLixcvztbFt/SORVLyLdRhYWEaOnSo2rdvryJFiujcuXOZumD9r3/9ywiOa9WqpX/+85+qVq2aIiMjtWLFCi1evFhhYWEaPny4/Pz80uyZ/v777+vEiRPq3bu3unXrplKlSunSpUspLtBaz0mcnJxUr169NNuWmJiohg0bqm3btqpTp45Kliyp+Ph4hYaGys/PT1u2bFFQUJDefPNNzZo1K8Pv2Z7x48fryJEj6tatm3r37q2SJUsqODhYv//+uw4dOqTdu3drzJgx+v7771OtIywsTC+99JKcnZ311ltv6dFHH5Wbm5v27t2r77//Xjdv3tR//vMftW7d2u5Esbn5fvOK7bmX9TiamqpVqyo4OFiXLl0ydaKwjplduHDhNL/rypQpIy8vL0VFRaVYt5T8/Xnp0qUMt8Xee7BtS2brOXPmTI6Hx9nZrsPDw/XUU0/p0qVLKlCggAYMGKDGjRvL29tb0dHR2rZtm2bOnKlz585p1KhRWrx4sQoXLiwpeQzeLl26ZOpcLiEhQRUqVFCnTp1Uv359lS9fXi4uLrp48aK2b9+uhQsXGncyLF++3Lgz7F7iqG3lftyPbDVo0MBY3rVrF+ExkIMIj4FccP369RQ/7iwWi27duqV9+/ZpxowZunPnjgoXLmw39MiIFi1aqGTJkrp+/bqWL1+eani8fft2Y2zWu8usWrVKUvLtP/Z6Frdu3VrPP/+8qWdtTliyZImk5F7Vtj2yKlWqpIYNG+rAgQNasmRJroTHf//9t4KDgyUl94K+u4defHy83nnnHcXHx+sf//iHpkyZkuKWsLp166pdu3Zq3Lixxo0bp7///lvbtm27p05uDh06pDZt2mjq1Kkperi1adNGNWrU0LfffquLFy9q6tSpdsdSywprDwPbE357k06WKlXKGG7Azc3NbpmcsHHjRp08eVJS8vAM9no7hoaGqkyZMpo3b16KgCa9HnS2vvvuOyM4fuGFF/T6668bz9WrV09dunTRO++8o2XLlmnfvn2aN2+ennrqKbt1RUREyNPTU3PmzFGtWrWMx21PvB3p559/lsVikZR6b5cTJ06oefPmmjZtWorbq609V27cuKHx48fLYrGoX79+mjhxYoptsG7duurcubPRe3nmzJkaOHBgih8dx48f1x9//GGUnzVrVoqeU82bN1ejRo2MIR+yasKECUZw/Pbbb2vUqFEpnm/QoIG6deumf/3rX8YYhtYJBw8fPmyUq1y5cobCYnt69OihlStXKioqShs2bFDXrl3tllu+fLmk5MDZOlO61fz587Vx40a5ublp6tSpat26dYrnfX191atXLw0ZMkQnT57UpEmTjEA1J4WGhqa42yQpKcnofT979mxJUo0aNTRixAi7r//+++915MgRFSlSRL/99pspjHzsscfUo0cPDRw4UFevXtV//vMf4xbeIkWKqEiRIukej2z1799fL7/8sululbp166pjx44aOnSoBgwYoCtXrujHH3/UF198kfEPw8aVK1eMINvJySnVHmEnT57Uzz//bIxHKSndQNbWxo0bjfMEe/tsq1at9Mgjj2jcuHGKiIjQ5MmTjQsi9hw/flyffPKJ+vfvbzxWt27dFGX27dsnKfkYaw2aUjNjxgy7k6o2atRIPXv21MKFC/Xee+9p165dCggIUPPmzdN7y6k6dOiQ3nzzTWOMUCn5s+zatauef/55bd26VWvXrtWmTZtSHXoiODhY3t7emjNnToqQvUGDBqpXr56efvppJSQkaN68efrggw9y5P1ahzTKDuvwTDnh8uXLxnJ6Q+RYv4MtFosuX76c4jvAOvFuuXLl0l3nQw89pJMnT6ZY991tSa8e2+cdVY81cMtJ2dmuP/nkE126dEne3t6aMWOGKehu2rSpunbtqiFDhuj8+fP65ZdfjAu2JUuWVMmSJTN1Lvfqq6+qQoUKpqE86tevry5duuipp57SoEGDdOPGDc2aNSvFuZOVveGIsiInhkaTHLet3I/7ka2iRYsaw8Dd3WsegGMxYR6QC+bMmaMePXoY/3r27KkhQ4boyy+/1PXr1zVo0CDNnz8/y7fJurq6GhPmbNu2LdVb0q0/MD09PU29s6w9BB977LE015XebfHZlZCQYNwq3aFDB9Ptcb169ZKUfJKb1pXo7IiLi9Pp06f1008/GWGoh4eH3Z6JK1as0IULF+Tu7q7PP/881bHEBgwYYIR0ixYtypF255QCBQro448/tjscwAsvvGCc5C9cuDDTY3bfS5KSknTx4kX9+uuvKX6IPPvss6m+5q233srymKZxcXHGBCA1atQwxgG15eTkpAkTJhj75Z9//plmnc8++2yK4NjR4uLidOLECY0fP96YoMXV1VXDhw+3W97Z2VmffPJJquNyzpkzR7du3VLZsmU1YcIEu9ugJL3yyisqW7askpKSjLFfrebOnWsMKzJx4kS7t9z27t3bFJJmxpkzZ7R27VpJyb1U7w6ObRUqVMju+MKO8I9//MPYFuz1jJWSe/7YjiNr2zvZYrHo559/lpQ8dndqn0nRokX1zjvvSEq+ndR6gS0nvffeeym+R3v16qWRI0dqxowZKliwoN544w3Nnj3b7hiXt2/fNvaN1157LdXQ1NvbWy+++KIkac2aNdkabsbHxyfNST7LlStnDEmwfv1640JLRlgsFoWHh2vlypUaPHiwbt68KSl5siLbORRs9enTJ0VwnFnWz8/NzU2TJ0+2u88OGDDAGHvc39/fuJhiT7NmzVIEx/ZYA4OM9Bq0F6Ta6tevnzGUhnVfzaqaNWvqueeeMz3u6uqqf//738bf3XpRIzUffPCB3TDnscceMy4y2t4qbis3329euX37trGc3hAgtuded++31noycsePtR7bdd/9//TqsX0+tbZkpJ603lNOyOp2HRoaalxYGjduXKo9pOvUqWNc3M7ueXDFihXTHAO6Zs2axvHFdozde4mjtpX7cT+6m/U7wtrZAkDOoOcxkMeskyu5u7vr7bffzvLkJj169NCsWbMUHx+vVatWmXof3rlzJ0W4cXfIWbp0aV28eFErV65U//79Uw1Bc9qWLVuM3tE9e/Y0Pf/4449r8uTJio+Pl5+fX7ZvNbeyNzmHVd26dfX+++/b7TFqDWEaN26c7sQcjz32mA4ePKj9+/dnq625rWXLlqn2VnB2dlbv3r31+eefKyIiQkFBQdkeKzQ/SWu7kKSBAwcaE1Dezc3Nze5s1Bl1+PBhIxTq06dPqsNReHl56fHHH9ecOXN06tQphYWFpXrrur19Kjt27dqV5mfk5uamjz/+ONVeRI0aNUqzl611/2rbtm2ax0ZXV1f5+vpqzZo1Rm9Fq+3bt0tK7imaVk/Lfv36afPmzak+n5ZNmzYZ4V9qQXlucHNzU9euXTV37lxt3rxZN2/eNE0E6O/vb4wje/f2cOrUKYWEhEhKvgslLbY9XPfv359umJWTbt26pfnz56tYsWJ298fdu3fr1q1bkjL+vuLj43XkyJF0x5rMqKioKIWHh+vOnTvGtmL9no2Kikp3TNO7J1a8W/369fXRRx+l+nxqdyRlREJCgnbv3i0p+fsgrXGl+/fvr+3btyshIUG7du1S9+7ds9we64XwzE7IarFYdO3aNUVFRSk+Pt54vGzZsjp69KhpTNbM6tOnT6rBVbly5dSyZUtt3LhRu3btUmJiot1jd5EiRdS2bdtU11G3bl3t378/Q2FIVt/vG2+8kWpP/YzKyXPF2NhYYzmtCzGSUnw/WI9vd9eTXh229diuW0o5mbUj2pLdenJCVrfrTZs2KTExUR4eHulehG3cuLF++eUXhYWF6eLFiw6ZMFRKHs8+MjJSsbGxxvHVetw4deqU4uPjTZ+3dTii/MrR27+j6skP+9HdrBfkrR2hAOQMwmMgF9jOHm51584dnTt3TkuXLtWMGTM0Y8YMHT58WNOnT8/SyXjDhg1VsWJFhYSEaNmyZabw2DqZnmT/R1vv3r01depU7du3Tx06dFDXrl3VvHlzPfroo7k6W7H1FsqSJUvaHdqhRIkSatWqlTZs2CA/Pz+9/vrrOToDtZubm/r165fqhBvW2823bt2abtBoda+d3KQ3nqntsAcnTpy4r8Jjezw8PNSoUSM9/fTTaU4WVrly5WzN+mwdFkNKf6iLhg0bGkMHnDx50m547OnpmeNjJloVL15c//jHPzRy5Mg0ezqntc8kJiYaoce8efOMiVPSY7t/xcXF6dy5c5Iytx1nVlBQkKTk40VmhiXJCT169NDcuXMVFxenNWvWmHp3WoesKFOmjGnSPtvhM+6e5CYtV69ezUaLM+buSQYtFouioqJ07NgxzZgxQ/7+/vrwww919uxZ063Itu8rM71vs/u+Lly4oF9//VUbNmxId6K68PDwTO+fLi4uqlWrlnr37q3Bgwen+WM8o99P9pw/f14xMTGS0t9PbLd/22NYVtpjHSYro+Hxxo0bNWfOHO3evdvU481WdicMTe9YUr9+fW3cuFHR0dE6f/683QsrlSpVkrNz6jeAWsOQtN5Hdt9v2bJl072NPS/Zfn/Gx8en+X1qG0oVLFjQVE9MTEyKYD29eu5el22QlV496bXFEfXkhKxu19bja0xMjOrUqZPh9V27di1b4fHx48f1+++/a8uWLWkeq5OSknTz5k3THQzW4YjyK0dtK/fjfnQ369/R+j0FIGcQHgN5pGDBgqpZs6bGjBmjypUra9y4cdqzZ49+/PHHLPem7dGjh77//nvt27dPoaGhKXr0+fn5SUoOZa23ldp68cUXdeXKFS1atEjXr1/Xn3/+adymWqNGDXXu3FlPPfVUlib0y6ibN28ak/J169Yt1VvUe/bsqQ0bNujixYvauXOnmjVrlu11297iffPmTeOkNCQkRBMnTlRMTIzd4QmskzRlRk70ILEN0DN6+3NGy6V3y7Dt87kxJnZust0uXFxcVKhQIZUuXTrVXsC2svujJDIy0lhO7wKO7X5p+zpHtseeevXqafLkycb/XV1dVbRo0QxPTpNWmyIjI42xgTPDdv+KjIw0tvP02pSdY5s1nClatGiW7x5xlEcffVTe3t66cOGC/Pz8UoTH169fV0BAgCTpiSeeMIVX1rs+Mis3esXdzcnJSYULF1bjxo3VuHFjvfXWW1q+fLl+//13tWnTJsX3XF68r02bNum1117L8I/Z9NY1adIkI9xxcnKSh4eHSpUqleFQKTtDpdgeU9Lbj2wnUkrr+yAj7XF3d1d8fLyp99rdLBaLPvjgA2OYn/Rkd3t1xPE4vU4C1n3TOuSOrdx+v3nF9hb727dvpxl62e5nd98OX6hQIcXExGRo6AdrPXff3m/7//TqsX3eXlsyWk9a7yknZHW7zurxNTtB3/z58zVhwoQMnyPci/uAo7aV+3E/upv1OyK1340AHIM9DMgHnnzySX311VeKiIjQwoULsx0eWywWrVixwpj0IiIiQlu3bpWUeijr5uamSZMmacSIEVq+fLl27Nihw4cPKz4+XidPntTJkyf122+/6YsvvlDHjh2z/mbTsHLlSuNK86xZszI0CcvSpUsdEh7ffVv9Y489pl69eumpp57S8ePH9fXXX6tJkyamXleJiYmSkicUtI4BmhdsTwbT+6FtZT0xS++kLCd7dud32ZmALyMBc0Y54m/gyPZYWSd8y6q02mTdt6TkW+HTu23fKrXelw/Kduzk5KTu3bvrp59+UmBgoK5cuWL0Lly1apXxY9veHSi2QdWPP/6Y6vi5d8sPM9k/++yzRq/qhQsXpgiPbbelxYsXZ/gHZkYmBrLnxo0bevvttxUTEyNPT0+NHDlSrVq1UsWKFeXl5WVcYAgICDCGOUnvYp6Pj0++OB45aj9Kq9etVYkSJRQVFZXuRckFCxYYQWrt2rX1zDPPqEGDBipbtqw8PDyM9z5mzBjTmOhZkdfHEke93ytXrqQabmeUh4dHjt3RYrv/XblyJc1w0zpJmJOTk2m/LVu2rK5du5bmpFt312OvDqv06klrUrCMTgJ29/NpDRXjKFndrq3H1+LFi2vmzJkZfl1WJ4Y9ffq0ERyXLFlSI0eOVLNmzeTt7a1ChQoZ5wALFizQ+++/L8n+8fXmzZsZ2ibSk1MTNTtqW7kf96O7WY9j+bknOXA/IDwG8gFnZ2dVqlRJERERunr1qsLDw1PMKp9RVapUUb169XT48GEtX77cCI/XrFlj3B6U3jiD1atXNyYDi42N1Z49e7Rs2TItXbpU0dHReuutt+Tv75/qmKrZsWTJkky/Zs2aNRo/fnyOjLvn5eWlzz//XH369FFCQoI+++wz04RkxYoVU1hYmOLj43PsBDIjbCcyzOit1tbb+9PrAZbeMBu2vU5yekLFB4nt3+X69euqUqVKqmVt/0Y5NRlbbrN9HxaLJUv7l+0PifS24+wMJ2M9XkdGRiouLi7Pex/36NFDP/30k5KSkrR8+XJjYjZruFq1alXVrVvX9Drb/bdw4cJ5ekzLLNtZ4U+cOJHiOdvv0xIlSmQ5FM6oNWvWGOOVf//993bv9pFS75Wa39jui+ntJ7bfP9n9PihRooRCQkKMzzI18+fPl5Q8FMTcuXNT7Y3tqM87r4/Hjnq/X3/9tTFUWFY1adIkQxf6s6JatWrG8pkzZ4wJAO05c+aMpOTg7O4L4tWrV9eRI0d069YtXb16NUXveFthYWGKiooyrVtKPh986KGHdOnSJWNd6bXFXj3Vq1e3Wy69emyPbzklq9u1dT+/ffu2qlWrliMXqm0tXrxYCQkJcnFx0axZs0yfsVV62//atWtNQxxlxfHjx7Ndhz2O2lbux/3obta/dW5cZAEeZOlf9geQK2xvvbLtJZVZ1nD4xIkTxnih1lvvK1asmKnxON3d3dWiRQtNnjxZY8aMkZR869fGjRuz3L7UhISEGBNdPfHEE/rPf/6T5j9r7+zbt2/L39/f4e2xqlWrljHhT2BgoGlCLev4bocPH04xPldusx0/8siRI+mWv3btmq5cuWJ6rT2HDh3K8PM1atRId92Olte9wHKK7Wd54MCBNMsePHjQ7uvuZQUKFDDey969e7NUh7u7uzEuY2a248yyBrHx8fFZmhDT0dtwjRo1jLGmrYHx+fPnjWNsahcRbX9UZvUzzyu236F338rsqPeV0b/TqVOnJCWHKqkFx1LKsZjzswoVKhgXaG2PNfY48lhkvXgREhJid/gGK+vYyu3bt081SLVYLBn6bsyI9I4V1r9rTvXKze33m1ds55rYtWtXquWuXr2q4OBgScmTsKZVj3XiR3tsn0urnrNnz6Z5kd62rXfX4+PjY3S+SKstts+XLVs2y710MyOr27X1PDguLi5bx7TMHl9r1aqVZqh4rxxfU+OobeV+3I9sJSUlGROL2gbuAByP8BjIB2JiYnT69GlJyWMhZ6XXsdUTTzxhXPVftmyZLl++rMDAQEnZm23ddmiI7E42Y49tr+MRI0boiSeeSPPfs88+a/R2cMRtqGkZPXq0cYvtDz/8kOI564Rpt27d0qJFi3K0HWmpXbu28Xn4+/unO3SF7Vi+zZs3T7Pstm3bFBYWZve5pKQko+dS0aJF7fZmzGnWXp55Gd7nhHr16hk9Z5csWZJqeBIVFaVVq1ZJSj5xzom7AvKKdf86c+aMtmzZkqU6rNv3iRMnjInt7Fm4cGGW6pekNm3aGD98Z8yYkenX2w4746jt2Hq8DwoK0unTp40Q2fa5u9WtW9folfvXX39leAic/MA2KLi791GLFi2M8HPmzJkZHu/9brY9ytP6O1nD69jY2FT325iYmBz/7nIUV1dXNW7cWFLy90Fatxtbh1NwdXVVkyZNsrVea8gQHR1tnCPZY73gntYYmuvWrXPYxI5Lly5NdRu6cuWKMUxYkyZNcqQXpqPe76effqrjx49n619O9TqWku+ms4aDq1evTnWMXNve0/aGVWvfvr1xDpfWcd56Dufs7Gx3MtwOHTrYXaetmJgYrV69WlLy9/HdPXmdnJyMes6cOZPqxcb9+/cbPS87dOiQKxfJs7pdt2vXLlvff1YZPZezHl/T2v7DwsK0fv36NOvp27dvtrf/nOp1LDluW7kf9yNbp06dMraFvJ6wGLjfER4D+cCUKVOMyRxatWqVrR8bpUuXNoLeFStWaNmyZcbJYGqBQUREhNavX5/mD+pt27YZy3df1Q4NDVXNmjVVs2ZNDR06NNNttlgsxoR+3t7eqlevXrqvcXV1NU5uAgICUg03HaFatWrq1KmTpOReazt27DCe69OnjxFUfPbZZ+n2DggMDEzzyn9Wubm5aeDAgZKSew9MmjQp1b/n8ePHNXXqVEnJY9b27ds3zbrj4uI0fvx4uz3ip02bZtwi3q9fvzy5Xd9669z169eNW+XuBwUKFNCTTz4pKTn4tP7NbFksFn388cfGBZ0hQ4bkahtz2rBhw4xbJ8eOHWv0uEvNxo0bjTsurAYNGmT8mBo3bpzdH5x+fn7atGlTlttZpUoV4xixdu1a/fLLL6mWjY6ONt1Oa3v7p7UHTXZ1797deN9+fn5asWKFJOmRRx5JtTeks7OzMdzR+fPnNWbMmDR/yEdFRemPP/6w+9zQoUON74XQ0NDsvJV0xcXF6b///a/x/zZt2qR4vkiRIsa+sW/fPk2aNCnNnqzXrl0zhgawZXthJiQkJNXXW3u7x8TEGBd2bCUmJuqDDz7I0e8tR7N+fvHx8Xr//feNobBsLViwwAiYOnXqlO0LWY899pixnFaP50qVKkmSNmzYYHd85JCQEH300UfZaouto0eP2t3HExIS9MEHHxifzeDBgx22Tlu5/X7z0ogRIyQln6d+8cUXpudDQkL0008/SUr+XKzHYVulS5c2zn+3bt1qhFK2Vq1aZWy7vXr1sntLfqdOnYxj508//WT3GPD5558bx3frcEF3e+aZZ4zz/I8//tg0mdudO3f08ccfS0o+133mmWfs1rNo0SLjGDtlyhS7ZTIjq9t11apV1bVrV0nJvzt+++23NNdz/vz5FBczrTJ6Lmc9vp47d87unSQxMTF666237slJ8u7mqG3lftyPrGy/G1q2bJlmWQDZw5jHQC64fv26aQzG2NhYnTt3TkuWLDF61Lm7u+vVV1/N9vp69Oihbdu26dKlS5o2bZqk5F6MqV25jYqK0gsvvCBvb2917txZDRo0kLe3t1xcXHT16lVt2LDB+CFdtmxZtW3bNttttLVnzx4jMOnSpUuGX9e5c2ctWLBAiYmJ8vPz07PPPuvQdtkaPXq01qxZIym597E1oC9QoIC++eYbDR06VNHR0XrmmWfUrVs3dezYUT4+PkpKStLVq1d15MgR+fv768SJExo3bly2e2Sl1kZ/f3+dOXNGc+fOVVBQkJ588kk9/PDDcnd319WrV7Vt2zb99ddfRs+DDz/8MN0JJurVq6cNGzZo8ODBGj58uCpVqqTr169ryZIlRiBVrlw5vfjiiw5/TxlhvZ0tKSlJH374oYYOHZqi9771h/a96KWXXpK/v7/Onz+vKVOm6MSJE+rbt69Kly6t0NBQ/fHHH8bFiEceecS4gHC/KFWqlD777DO9+uqrunr1qvr166c+ffqodevWKleunBISEnT58mUdPHhQa9as0fnz5/Xjjz8aQzZIybe2DhkyRH/88YcOHz6sfv36adSoUXr44Yd169YtrV69Wn/99ZcxXnxWffjhh9q/f7/CwsL0xRdfaMuWLerTp4+qVq0qJycnXbhwQTt37tTKlSv17bffqmnTpsZra9euLXd3d8XGxuq///2vXF1dVb58eaOXT9myZVO9PT015cqVU+PGjbVr1y7Nnj3bGDc2vTtQBg8erO3bt8vf31+rV69WUFCQBg4cqAYNGqhw4cKKiorSmTNntGvXLq1fv14FChTQ008/nclPK/NCQ0NNd+VERUXp6NGjmjNnjnFhoVKlSnb3g9dee027d+/WgQMHNHPmTO3atUsDBgxQrVq15OnpqcjISJ06dUrbt2/X5s2b9fDDD6t///4p6njkkUeM5cmTJ2v06NEqXbq0EdJ7e3vL1dVVjz/+uP7zn/8oLi5OY8eO1dGjR9WyZUt5eXnp1KlTmjVrlo4cOaJGjRrdM8ODtG3bVl27dtXq1au1detWDRw4UMOHD1fVqlV18+ZNrVixwuiNVqxYMYeMJerj46OaNWvq+PHjCggIUL9+/eyW6927tz7//HOFhYVp4MCBxv4dGxurHTt2aMaMGYqLi1PdunUdMpRDvXr19OWXX+rYsWPq1auXSpYsqXPnzum3334zgox27dqpXbt22V6XPbn9frNq9erVKS7W7dmzx+6ylHysb926tamOPn36aOHChdq7d6/+/PNPXbt2Tf3791fRokV18OBBTZ06VVFRUXJ2dtb777+f6mSYb7zxhrZs2aIbN27orbfe0uHDh41z2Y0bNxqBZ4kSJYx5P+7m5uamcePGafTo0YqKitLgwYP1wgsvqEGDBoqMjNT8+fON88RHH31UvXr1sltPlSpVNHLkSE2bNk2HDx/W4MGDNWrUKFWoUEHnz5/Xzz//bNwlM3LkSCMszWnZ2a4nTJigw4cP6/z58/r000+1bt069erVSzVq1FCBAgUUERGhY8eOacuWLdqxY4c6depkDAlnldFzuZ49e2rWrFlKSkrS888/r5EjR+rRRx+Vu7u7Dh8+rBkzZig4ODjPj6+BgYEpglHbuzbPnTtnulvRXkcOR20r9+N+ZBUQECAp+VwvpybvBJCM8BjIBXPmzNGcOXPSLFOiRAl98cUX6Y4/mxGdOnXShAkTdOfOnQwHBpJ04cKFNHsMlC5dWlOnTlWhQoWy3UZbtkNWZCY8btGihYoUKaKbN29q6dKlORoe16lTR23atNGmTZu0Y8cO7d+/X76+vpIkX19fzZo1S6+//rouXbqkZcuWpRgW4m5eXl450kZPT0/NmDFDr776qvbt26eDBw+m2lvL3d1d48aNU+/evdOtd8iQIdq9e7cWLVpkjDVtq3Tp0po+fboKFy6c3beQJc2aNZOvr6/279+v5cuXm3q05ORthTnNy8tLv//+u0aNGqUzZ85ozZo1xkm1rUaNGumHH37I8Ylq8kLnzp01depUjR07VhEREZo7d67mzp1rt6yzs7PdyTPfffddhYWF6e+//9aZM2dMwZaPj4+++eYbu7dqZlSpUqU0e/Zsvfjiizpx4oR27NiR4i6FtHh5eWno0KH65ZdfdOTIEaOXkNXMmTNThM0Z1bNnT+3atcv4HrAGm2lxcnLS119/rX//+9+aO3euQkJC7PZUskpt5nZrDyk3NzeHHPPee++9dMvUqlVL33//vd2gvUCBAvr11181duxY/f333zp27JgmTpyYal322lypUiU9/vjjRu8qaw8rq3Xr1snHx0flypXThAkT9MEHHyg2NlY///yzfv755xRlu3XrpgEDBmj48OHpvq/84vPPP1diYqL8/f115MgRvfPOO6YyZcqU0bRp01S2bFmHrHPAgAH6+OOPtW7dOsXExNjdv4cNG6bt27d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\n",
      "text/plain": [
       "<Figure size 700x700 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 711,
       "width": 711
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(2, 1, figsize=(7, 7), sharex=True)\n",
    "az.plot_posterior(weak_prior_predictive[\"reluplift_b\"], textsize=10, ax=axs[0], kind=\"hist\")\n",
    "axs[0].set_title(f\"B vs. A Rel Uplift Prior Predictive, {weak_prior.priors}\", fontsize=10)\n",
    "axs[0].axvline(x=0, color=\"red\")\n",
    "az.plot_posterior(strong_prior_predictive[\"reluplift_b\"], textsize=10, ax=axs[1], kind=\"hist\")\n",
    "axs[1].set_title(f\"B vs. A Rel Uplift Prior Predictive, {strong_prior.priors}\", fontsize=10)\n",
    "axs[1].axvline(x=0, color=\"red\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f7757126",
   "metadata": {},
   "source": [
    "With the weak prior our 94% HDI for the relative uplift for B over A is roughly [-20%, +20%], whereas it is roughly [-2%, +2%] with the strong prior. This is effectively the \"starting point\" for the relative uplift distribution, and will affect how the observed conversions translate to the posterior distribution.\n",
    "\n",
    "How we choose these priors in practice depends on broader context of the company running the A/B tests. A strong prior can help guard against false discoveries, but may require more data to detect winning variants when they exist (and more data = more time required running the test). A weak prior gives more weight to the observed data, but could also lead to more false discoveries as a result of early stopping issues.\n",
    "\n",
    "Below we'll walk through the inference results from two different prior choices."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "87c03f75",
   "metadata": {},
   "source": [
    "#### Data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b999654",
   "metadata": {},
   "source": [
    "We generate two datasets: one where the \"true\" conversion rate of each variant is the same, and one where variant B has a higher true conversion rate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "7631f294",
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_binomial_data(\n",
    "    variants: List[str], true_rates: List[str], samples_per_variant: int = 100000\n",
    ") -> pd.DataFrame:\n",
    "    data = {}\n",
    "    for variant, p in zip(variants, true_rates):\n",
    "        data[variant] = bernoulli.rvs(p, size=samples_per_variant)\n",
    "    agg = (\n",
    "        pd.DataFrame(data)\n",
    "        .aggregate([\"count\", \"sum\"])\n",
    "        .rename(index={\"count\": \"trials\", \"sum\": \"successes\"})\n",
    "    )\n",
    "    return agg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "5ff1e081",
   "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>A</th>\n",
       "      <th>B</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>trials</th>\n",
       "      <td>100000</td>\n",
       "      <td>100000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>successes</th>\n",
       "      <td>23110</td>\n",
       "      <td>22688</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                A       B\n",
       "trials     100000  100000\n",
       "successes   23110   22688"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Example generated data\n",
    "generate_binomial_data([\"A\", \"B\"], [0.23, 0.23])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "74f9d751",
   "metadata": {},
   "source": [
    "We'll also write a function to wrap the data generation, sampling, and posterior plots so that we can easily compare the results of both models (strong and weak prior) under both scenarios (same true rate vs. different true rate)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "0030ee2b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_scenario_twovariant(\n",
    "    variants: List[str],\n",
    "    true_rates: List[float],\n",
    "    samples_per_variant: int,\n",
    "    weak_prior: BetaPrior,\n",
    "    strong_prior: BetaPrior,\n",
    ") -> None:\n",
    "    generated = generate_binomial_data(variants, true_rates, samples_per_variant)\n",
    "    data = [BinomialData(**generated[v].to_dict()) for v in variants]\n",
    "    with ConversionModelTwoVariant(priors=weak_prior).create_model(data):\n",
    "        trace_weak = pm.sample(draws=5000, return_inferencedata=True, cores=1, chains=2)\n",
    "    with ConversionModelTwoVariant(priors=strong_prior).create_model(data):\n",
    "        trace_strong = pm.sample(draws=5000, return_inferencedata=True, cores=1, chains=2)\n",
    "\n",
    "    true_rel_uplift = true_rates[1] / true_rates[0] - 1\n",
    "\n",
    "    fig, axs = plt.subplots(2, 1, figsize=(7, 7), sharex=True)\n",
    "    az.plot_posterior(trace_weak.posterior[\"reluplift_b\"], textsize=10, ax=axs[0], kind=\"hist\")\n",
    "    axs[0].set_title(f\"True Rel Uplift = {true_rel_uplift:.1%}, {weak_prior}\", fontsize=10)\n",
    "    axs[0].axvline(x=0, color=\"red\")\n",
    "    az.plot_posterior(trace_strong.posterior[\"reluplift_b\"], textsize=10, ax=axs[1], kind=\"hist\")\n",
    "    axs[1].set_title(f\"True Rel Uplift = {true_rel_uplift:.1%}, {strong_prior}\", fontsize=10)\n",
    "    axs[1].axvline(x=0, color=\"red\")\n",
    "    fig.suptitle(\"B vs. A Rel Uplift\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4385419f",
   "metadata": {},
   "source": [
    "#### Scenario 1 - same underlying conversion rates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "1f72ff74",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Sequential sampling (2 chains in 1 job)\n",
      "NUTS: [p]\n"
     ]
    },
    {
     "data": {
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       "                border: none;\n",
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\n",
      "text/plain": [
       "<Figure size 700x700 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 711,
       "width": 711
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "run_scenario_twovariant(\n",
    "    variants=[\"A\", \"B\"],\n",
    "    true_rates=[0.23, 0.23],\n",
    "    samples_per_variant=100000,\n",
    "    weak_prior=BetaPrior(alpha=100, beta=100),\n",
    "    strong_prior=BetaPrior(alpha=10000, beta=10000),\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eefc18cc",
   "metadata": {},
   "source": [
    "* In both cases, the true uplift of 0% lies within the 94% HDI.\n",
    "* We can then use this relative uplift distribution to make a decision about whether to apply the new landing page / features in Variant B as the default. For example, we can decide that if the 94% HDI is above 0, we would roll out Variant B. In this case, 0 is in the HDI, so the decision would be to _not_ roll out Variant B."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9935152f",
   "metadata": {},
   "source": [
    "#### Scenario 2 - different underlying rates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "7e52fc97",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Sequential sampling (2 chains in 1 job)\n",
      "NUTS: [p]\n"
     ]
    },
    {
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       "                border: none;\n",
       "                /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
       "                background-size: auto;\n",
       "            }\n",
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       "      100.00% [6000/6000 00:02<00:00 Sampling chain 0, 0 divergences]\n",
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       "    "
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    {
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       "                border: none;\n",
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       "      100.00% [6000/6000 00:02<00:00 Sampling chain 1, 0 divergences]\n",
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    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 2 chains for 1_000 tune and 5_000 draw iterations (2_000 + 10_000 draws total) took 5 seconds.\n",
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Sequential sampling (2 chains in 1 job)\n",
      "NUTS: [p]\n"
     ]
    },
    {
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       "\n",
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       "                border: none;\n",
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       "      <progress value='6000' class='' max='6000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
       "      100.00% [6000/6000 00:02<00:00 Sampling chain 0, 0 divergences]\n",
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       "      100.00% [6000/6000 00:02<00:00 Sampling chain 1, 0 divergences]\n",
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    {
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     "output_type": "stream",
     "text": [
      "Sampling 2 chains for 1_000 tune and 5_000 draw iterations (2_000 + 10_000 draws total) took 4 seconds.\n"
     ]
    },
    {
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\n",
      "text/plain": [
       "<Figure size 700x700 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 711,
       "width": 711
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "run_scenario_twovariant(\n",
    "    variants=[\"A\", \"B\"],\n",
    "    true_rates=[0.21, 0.23],\n",
    "    samples_per_variant=100000,\n",
    "    weak_prior=BetaPrior(alpha=100, beta=100),\n",
    "    strong_prior=BetaPrior(alpha=10000, beta=10000),\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f62643de",
   "metadata": {},
   "source": [
    "* In both cases, the posterior relative uplift distribution suggests that B has a higher conversion rate than A, as the 94% HDI is well above 0. The decision in this case would be to roll out Variant B to all users, and this outcome \"true discovery\".\n",
    "* That said, in practice are usually also interested in _how much better_ Variant B is. For the model with the strong prior, the prior is effectively pulling the relative uplift distribution closer to 0, so our central estimate of the relative uplift is **conservative (i.e. understated)**. We would need much more data for our inference to get closer to the true relative uplift of 9.5%.\n",
    "\n",
    "The above examples demonstrate how to calculate perform A/B testing analysis for a two-variant test with the simple Beta-Binomial model, and the benefits and disadvantages of choosing a weak vs. strong prior. In the next section we provide a guide for handling a multi-variant (\"A/B/n\") test."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c871fb6e",
   "metadata": {},
   "source": [
    "### Generalising to multi-variant tests "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "724802d2",
   "metadata": {},
   "source": [
    "We'll continue using Bernoulli conversions and the Beta-Binomial model in this section for simplicity. The focus is on how to analyse tests with 3 or more variants - e.g. instead of just having one different landing page to test, we have multiple ideas we want to test at once. How can we tell if there's a winner amongst all of them?\n",
    "\n",
    "There are two main approaches we can take here:\n",
    "\n",
    "1. Take A as the 'control'. Compare the other variants (B, C, etc.) against A, one at a time.\n",
    "2. For each variant, compare against the `max()` of the other variants.\n",
    "\n",
    "Approach 1 is intuitive to most people, and is easily explained. But what if there are two variants that both beat the control, and we want to know which one is better? We can't make that inference with the individual uplift distributions. Approach 2 does handle this case - it effectively tries to find whether there is a clear winner or clear loser(s) amongst all the variants.\n",
    "\n",
    "We'll implement the model setup for both approaches below, cleaning up our code from before so that it generalises to the `n` variant case. Note that we can also re-use this model for the 2-variant case."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "2023b905",
   "metadata": {},
   "outputs": [],
   "source": [
    "class ConversionModel:\n",
    "    def __init__(self, priors: BetaPrior):\n",
    "        self.priors = priors\n",
    "\n",
    "    def create_model(self, data: List[BinomialData], comparison_method) -> pm.Model:\n",
    "        num_variants = len(data)\n",
    "        trials = [d.trials for d in data]\n",
    "        successes = [d.successes for d in data]\n",
    "        with pm.Model() as model:\n",
    "            p = pm.Beta(\"p\", alpha=self.priors.alpha, beta=self.priors.beta, shape=num_variants)\n",
    "            y = pm.Binomial(\"y\", n=trials, p=p, observed=successes, shape=num_variants)\n",
    "            reluplift = []\n",
    "            for i in range(num_variants):\n",
    "                if comparison_method == \"compare_to_control\":\n",
    "                    comparison = p[0]\n",
    "                elif comparison_method == \"best_of_rest\":\n",
    "                    others = [p[j] for j in range(num_variants) if j != i]\n",
    "                    if len(others) > 1:\n",
    "                        comparison = pmm.maximum(*others)\n",
    "                    else:\n",
    "                        comparison = others[0]\n",
    "                else:\n",
    "                    raise ValueError(f\"comparison method {comparison_method} not recognised.\")\n",
    "                reluplift.append(pm.Deterministic(f\"reluplift_{i}\", p[i] / comparison - 1))\n",
    "        return model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "58ba7529",
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_scenario_bernoulli(\n",
    "    variants: List[str],\n",
    "    true_rates: List[float],\n",
    "    samples_per_variant: int,\n",
    "    priors: BetaPrior,\n",
    "    comparison_method: str,\n",
    ") -> az.InferenceData:\n",
    "    generated = generate_binomial_data(variants, true_rates, samples_per_variant)\n",
    "    data = [BinomialData(**generated[v].to_dict()) for v in variants]\n",
    "    with ConversionModel(priors).create_model(data=data, comparison_method=comparison_method):\n",
    "        trace = pm.sample(draws=5000, return_inferencedata=True, chains=2, cores=1)\n",
    "\n",
    "    n_plots = len(variants)\n",
    "    fig, axs = plt.subplots(nrows=n_plots, ncols=1, figsize=(3 * n_plots, 7), sharex=True)\n",
    "    for i, variant in enumerate(variants):\n",
    "        if i == 0 and comparison_method == \"compare_to_control\":\n",
    "            axs[i].set_yticks([])\n",
    "        else:\n",
    "            az.plot_posterior(\n",
    "                trace.posterior[f\"reluplift_{i}\"], textsize=10, ax=axs[i], kind=\"hist\"\n",
    "            )\n",
    "        axs[i].set_title(f\"Rel Uplift {variant}, True Rate = {true_rates[i]:.2%}\", fontsize=10)\n",
    "        axs[i].axvline(x=0, color=\"red\")\n",
    "    fig.suptitle(f\"Method {comparison_method}, {priors}\")\n",
    "\n",
    "    return trace"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b8c36ecc",
   "metadata": {},
   "source": [
    "We generate data where variants B and C are well above A, but quite close to each other:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "55ea29a9",
   "metadata": {},
   "outputs": [
    {
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      "NUTS: [p]\n"
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    },
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\n",
      "text/plain": [
       "<Figure size 900x700 with 3 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 711,
       "width": 911
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = run_scenario_bernoulli(\n",
    "    variants=[\"A\", \"B\", \"C\"],\n",
    "    true_rates=[0.21, 0.23, 0.228],\n",
    "    samples_per_variant=100000,\n",
    "    priors=BetaPrior(alpha=5000, beta=5000),\n",
    "    comparison_method=\"compare_to_control\",\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c1c2d20",
   "metadata": {},
   "source": [
    "* The relative uplift posteriors for both B and C show that they are clearly better than A (94% HDI well above 0), by roughly 7-8% relative.\n",
    "* However, we can't infer whether there is a winner between B and C."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "3cdb6808",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Sequential sampling (2 chains in 1 job)\n",
      "NUTS: [p]\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "    <div>\n",
       "        <style>\n",
       "            /* Turns off some styling */\n",
       "            progress {\n",
       "                /* gets rid of default border in Firefox and Opera. */\n",
       "                border: none;\n",
       "                /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
       "                background-size: auto;\n",
       "            }\n",
       "            .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
       "                background: #F44336;\n",
       "            }\n",
       "        </style>\n",
       "      <progress value='6000' class='' max='6000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
       "      100.00% [6000/6000 00:02<00:00 Sampling chain 0, 0 divergences]\n",
       "    </div>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "    <div>\n",
       "        <style>\n",
       "            /* Turns off some styling */\n",
       "            progress {\n",
       "                /* gets rid of default border in Firefox and Opera. */\n",
       "                border: none;\n",
       "                /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
       "                background-size: auto;\n",
       "            }\n",
       "            .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
       "                background: #F44336;\n",
       "            }\n",
       "        </style>\n",
       "      <progress value='6000' class='' max='6000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
       "      100.00% [6000/6000 00:02<00:00 Sampling chain 1, 0 divergences]\n",
       "    </div>\n",
       "    "
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 2 chains for 1_000 tune and 5_000 draw iterations (2_000 + 10_000 draws total) took 5 seconds.\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 900x700 with 3 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 711,
       "width": 911
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = run_scenario_bernoulli(\n",
    "    variants=[\"A\", \"B\", \"C\"],\n",
    "    true_rates=[0.21, 0.23, 0.228],\n",
    "    samples_per_variant=100000,\n",
    "    priors=BetaPrior(alpha=5000, beta=5000),\n",
    "    comparison_method=\"best_of_rest\",\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c883952",
   "metadata": {},
   "source": [
    "* The uplift plot for A tells us that it's a clear loser compared to variants B and C (94% HDI for A's relative uplift is well below 0).\n",
    "* Note that the relative uplift calculations for B and C are effectively ignoring variant A. This is because, say, when we are calculating `reluplift` for B, the maximum of the other variants will likely be variant C. Similarly when we are calculating `reluplift` for C, it is likely being compared to B.\n",
    "* The uplift plots for B and C tell us that we can't yet call a clear winner between the two variants, as the 94% HDI still overlaps with 0. We'd need a larger sample size to detect the 23% vs 22.8% conversion rate difference.\n",
    "* One disadvantage of this approach is that we can't directly say what the uplift of these variants is over variant A (the control). This number is often important in practice, as it allows us to estimate the overall impact if the A/B test changes were rolled out to all visitors. We _can_ get this number approximately though, by reframing the question to be \"how much worse is A compared to the other two variants\" (which is shown in Variant A's relative uplift distribution)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "90791ebd",
   "metadata": {},
   "source": [
    "### Value Conversions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "635ee63e",
   "metadata": {},
   "source": [
    "Now what if we wanted to compare A/B test variants in terms of how much revenue they generate, and/or estimate how much additional revenue a winning variant brings? We can't use a Beta-Binomial model for this, as the possible values for each visitor are now in the range `[0, Inf)`. The model proposed in the VWO paper is as follows:\n",
    "\n",
    "The revenue generated by an individual visitor is `revenue = probability of paying at all * mean amount spent when paying`:\n",
    "\n",
    "$$\\mathrm{Revenue}_i = \\mathrm{Bernoulli}(\\theta)_i * \\mathrm{Exponential}(\\lambda)_i I(\\mathrm{Bernoulli}(\\theta)_i = 1)$$\n",
    "\n",
    "We assume that the probability of paying at all is independent to the mean amount spent when paying. This is a typical assumption in practice, unless we have reason to believe that the two parameters have dependencies. With this, we can create separate models for the total number of visitors paying, and the total amount spent amongst the purchasing visitors (assuming independence between the behaviour of each visitor):\n",
    "\n",
    "$$c \\sim \\sum^N\\mathrm{Bernoulli}(\\theta) = \\mathrm{Binomial}(N, \\theta)$$\n",
    "\n",
    "$$r \\sim \\sum^K\\mathrm{Exponential}(\\lambda) = \\mathrm{Gamma}(K, \\lambda)$$\n",
    "\n",
    "where $N$ is the total number of visitors, $K$ is the total number of visitors with at least one purchase.\n",
    "\n",
    "We can re-use our Beta-Binomial model from before to model the Bernoulli conversions. For the mean purchase amount, we use a Gamma prior (which is also a conjugate prior to the Gamma likelihood). So in a two-variant test, the setup is:\n",
    "\n",
    "$$\\theta_A \\sim \\theta_B \\sim \\mathrm{Beta}(\\alpha_1, \\beta_1)$$\n",
    "$$\\lambda_A \\sim \\lambda_B \\sim \\mathrm{Gamma}(\\alpha_2, \\beta_2)$$\n",
    "$$c_A \\sim \\mathrm{Binomial}(N_A, \\theta_A), c_B \\sim \\mathrm{Binomial}(N_B, \\theta_B)$$\n",
    "$$r_A \\sim \\mathrm{Gamma}(c_A, \\lambda_A), r_B \\sim \\mathrm{Gamma}(c_B, \\lambda_B)$$\n",
    "$$\\mu_A = \\theta_A * \\dfrac{1}{\\lambda_A}, \\mu_B = \\theta_B * \\dfrac{1}{\\lambda_B}$$\n",
    "$$\\mathrm{reluplift}_B = \\mu_B / \\mu_A - 1$$\n",
    "\n",
    "$\\mu$ here represents the average revenue per visitor, including those who don't make a purchase. This is the best way to capture the overall revenue effect - some variants may increase the average sales value, but reduce the proportion of visitors that pay at all (e.g. if we promoted more expensive items on the landing page).\n",
    "\n",
    "Below we put the model setup into code and perform prior predictive checks."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "46f94b80",
   "metadata": {},
   "outputs": [],
   "source": [
    "@dataclass\n",
    "class GammaPrior:\n",
    "    alpha: float\n",
    "    beta: float"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "49ec3cc7",
   "metadata": {},
   "outputs": [],
   "source": [
    "@dataclass\n",
    "class RevenueData:\n",
    "    visitors: int\n",
    "    purchased: int\n",
    "    total_revenue: float"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "cf970faf",
   "metadata": {},
   "outputs": [],
   "source": [
    "class RevenueModel:\n",
    "    def __init__(self, conversion_rate_prior: BetaPrior, mean_purchase_prior: GammaPrior):\n",
    "        self.conversion_rate_prior = conversion_rate_prior\n",
    "        self.mean_purchase_prior = mean_purchase_prior\n",
    "\n",
    "    def create_model(self, data: List[RevenueData], comparison_method: str) -> pm.Model:\n",
    "        num_variants = len(data)\n",
    "        visitors = [d.visitors for d in data]\n",
    "        purchased = [d.purchased for d in data]\n",
    "        total_revenue = [d.total_revenue for d in data]\n",
    "\n",
    "        with pm.Model() as model:\n",
    "            theta = pm.Beta(\n",
    "                \"theta\",\n",
    "                alpha=self.conversion_rate_prior.alpha,\n",
    "                beta=self.conversion_rate_prior.beta,\n",
    "                shape=num_variants,\n",
    "            )\n",
    "            lam = pm.Gamma(\n",
    "                \"lam\",\n",
    "                alpha=self.mean_purchase_prior.alpha,\n",
    "                beta=self.mean_purchase_prior.beta,\n",
    "                shape=num_variants,\n",
    "            )\n",
    "            converted = pm.Binomial(\n",
    "                \"converted\", n=visitors, p=theta, observed=purchased, shape=num_variants\n",
    "            )\n",
    "            revenue = pm.Gamma(\n",
    "                \"revenue\", alpha=purchased, beta=lam, observed=total_revenue, shape=num_variants\n",
    "            )\n",
    "            revenue_per_visitor = pm.Deterministic(\"revenue_per_visitor\", theta * (1 / lam))\n",
    "            theta_reluplift = []\n",
    "            reciprocal_lam_reluplift = []\n",
    "            reluplift = []\n",
    "            for i in range(num_variants):\n",
    "                if comparison_method == \"compare_to_control\":\n",
    "                    comparison_theta = theta[0]\n",
    "                    comparison_lam = 1 / lam[0]\n",
    "                    comparison_rpv = revenue_per_visitor[0]\n",
    "                elif comparison_method == \"best_of_rest\":\n",
    "                    others_theta = [theta[j] for j in range(num_variants) if j != i]\n",
    "                    others_lam = [1 / lam[j] for j in range(num_variants) if j != i]\n",
    "                    others_rpv = [revenue_per_visitor[j] for j in range(num_variants) if j != i]\n",
    "                    if len(others_rpv) > 1:\n",
    "                        comparison_theta = pmm.maximum(*others_theta)\n",
    "                        comparison_lam = pmm.maximum(*others_lam)\n",
    "                        comparison_rpv = pmm.maximum(*others_rpv)\n",
    "                    else:\n",
    "                        comparison_theta = others_theta[0]\n",
    "                        comparison_lam = others_lam[0]\n",
    "                        comparison_rpv = others_rpv[0]\n",
    "                else:\n",
    "                    raise ValueError(f\"comparison method {comparison_method} not recognised.\")\n",
    "                theta_reluplift.append(\n",
    "                    pm.Deterministic(f\"theta_reluplift_{i}\", theta[i] / comparison_theta - 1)\n",
    "                )\n",
    "                reciprocal_lam_reluplift.append(\n",
    "                    pm.Deterministic(\n",
    "                        f\"reciprocal_lam_reluplift_{i}\", (1 / lam[i]) / comparison_lam - 1\n",
    "                    )\n",
    "                )\n",
    "                reluplift.append(\n",
    "                    pm.Deterministic(f\"reluplift_{i}\", revenue_per_visitor[i] / comparison_rpv - 1)\n",
    "                )\n",
    "        return model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8c439d5",
   "metadata": {},
   "source": [
    "For the Beta prior, we can set a similar prior to before - centered around 0.5, with the magnitude of `alpha` and `beta` determining how \"thin\" the distribution is.\n",
    "\n",
    "We need to be a bit more careful about the Gamma prior. The mean of the Gamma prior is $\\dfrac{\\alpha_G}{\\beta_G}$, and needs to be set to a reasonable value given existing mean purchase values. For example, if `alpha` and `beta` were set such that the mean was \\\\$1, but the average revenue per visitor for a website is much higher at \\\\$100, this could affect our inference."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "7483a55e",
   "metadata": {},
   "outputs": [],
   "source": [
    "c_prior = BetaPrior(alpha=5000, beta=5000)\n",
    "mp_prior = GammaPrior(alpha=9000, beta=900)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "07f83462",
   "metadata": {},
   "outputs": [],
   "source": [
    "data = [\n",
    "    RevenueData(visitors=1, purchased=1, total_revenue=1),\n",
    "    RevenueData(visitors=1, purchased=1, total_revenue=1),\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "f2b0d0c8",
   "metadata": {},
   "outputs": [],
   "source": [
    "with RevenueModel(c_prior, mp_prior).create_model(data, \"best_of_rest\"):\n",
    "    revenue_prior_predictive = pm.sample_prior_predictive(samples=10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "006b62e2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x138335970>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 491,
       "width": 783
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "az.plot_posterior(revenue_prior_predictive[\"reluplift_1\"], textsize=10, ax=ax, kind=\"hist\")\n",
    "ax.set_title(f\"Revenue Rel Uplift Prior Predictive, {c_prior}, {mp_prior}\", fontsize=10)\n",
    "ax.axvline(x=0, color=\"red\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d143b491",
   "metadata": {},
   "source": [
    "Similar to the model for Bernoulli conversions, the width of the prior predictive uplift distribution will depend on the strength of our priors. See the Bernoulli conversions section for a discussion of the benefits and disadvantages of using a weak vs. strong prior.\n",
    "\n",
    "Next we generate synthetic data for the model. We'll generate the following scenarios:\n",
    "\n",
    "* Same propensity to purchase and same mean purchase value.\n",
    "* Lower propensity to purchase and higher mean purchase value, but overall same revenue per visitor.\n",
    "* Higher propensity to purchase and higher mean purchase value, and overall higher revenue per visitor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "1e109784",
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_revenue_data(\n",
    "    variants: List[str],\n",
    "    true_conversion_rates: List[float],\n",
    "    true_mean_purchase: List[float],\n",
    "    samples_per_variant: int,\n",
    ") -> pd.DataFrame:\n",
    "    converted = {}\n",
    "    mean_purchase = {}\n",
    "    for variant, p, mp in zip(variants, true_conversion_rates, true_mean_purchase):\n",
    "        converted[variant] = bernoulli.rvs(p, size=samples_per_variant)\n",
    "        mean_purchase[variant] = expon.rvs(scale=mp, size=samples_per_variant)\n",
    "    converted = pd.DataFrame(converted)\n",
    "    mean_purchase = pd.DataFrame(mean_purchase)\n",
    "    revenue = converted * mean_purchase\n",
    "    agg = pd.concat(\n",
    "        [\n",
    "            converted.aggregate([\"count\", \"sum\"]).rename(\n",
    "                index={\"count\": \"visitors\", \"sum\": \"purchased\"}\n",
    "            ),\n",
    "            revenue.aggregate([\"sum\"]).rename(index={\"sum\": \"total_revenue\"}),\n",
    "        ]\n",
    "    )\n",
    "    return agg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "5e2d75f4",
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_scenario_value(\n",
    "    variants: List[str],\n",
    "    true_conversion_rates: List[float],\n",
    "    true_mean_purchase: List[float],\n",
    "    samples_per_variant: int,\n",
    "    conversion_rate_prior: BetaPrior,\n",
    "    mean_purchase_prior: GammaPrior,\n",
    "    comparison_method: str,\n",
    ") -> az.InferenceData:\n",
    "    generated = generate_revenue_data(\n",
    "        variants, true_conversion_rates, true_mean_purchase, samples_per_variant\n",
    "    )\n",
    "    data = [RevenueData(**generated[v].to_dict()) for v in variants]\n",
    "    with RevenueModel(conversion_rate_prior, mean_purchase_prior).create_model(\n",
    "        data, comparison_method\n",
    "    ):\n",
    "        trace = pm.sample(draws=5000, return_inferencedata=True, chains=2, cores=1)\n",
    "\n",
    "    n_plots = len(variants)\n",
    "    fig, axs = plt.subplots(nrows=n_plots, ncols=1, figsize=(3 * n_plots, 7), sharex=True)\n",
    "    for i, variant in enumerate(variants):\n",
    "        if i == 0 and comparison_method == \"compare_to_control\":\n",
    "            axs[i].set_yticks([])\n",
    "        else:\n",
    "            az.plot_posterior(\n",
    "                trace.posterior[f\"reluplift_{i}\"], textsize=10, ax=axs[i], kind=\"hist\"\n",
    "            )\n",
    "        true_rpv = true_conversion_rates[i] * true_mean_purchase[i]\n",
    "        axs[i].set_title(f\"Rel Uplift {variant}, True RPV = {true_rpv:.2f}\", fontsize=10)\n",
    "        axs[i].axvline(x=0, color=\"red\")\n",
    "    fig.suptitle(f\"Method {comparison_method}, {conversion_rate_prior}, {mean_purchase_prior}\")\n",
    "\n",
    "    return trace"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "975d4114",
   "metadata": {},
   "source": [
    "#### Scenario 1 - same underlying purchase rate and mean purchase value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "e4d49ea2",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
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      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Sequential sampling (2 chains in 1 job)\n",
      "NUTS: [lam, theta]\n"
     ]
    },
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     "data": {
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      "Sampling 2 chains for 1_000 tune and 5_000 draw iterations (2_000 + 10_000 draws total) took 6 seconds.\n"
     ]
    },
    {
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qM1NTU9StWxdLlizB5cuX8yx/OuUPdevWxebNm+UanjUFJr9mXl5ewvHbpk0bpg/9DwsPD8e+ffuE57LUgOJjBchs09iwYQO+++474e/EdWJWskZpmV9++QWDBw+WaxcxNjbG4MGD8fPPPwuvrV27FqmpqSrX+9dffwkpQmvXro3ly5crzK3UsGFDrFixQnh+/PhxBAUFqVznoUOH8O7dOwCAjY0Ntm3bJtdoDQBlypTB1q1bhYxHwcHBOHr0qMp10n/LmjVrhMeNGjXCihUrFDq6mZubY/LkyRgwYACAzGwjK1euVLvegrS/Fy5cWLj+DQ4OxvXr19Uurwt51spqZ2eHH3/8EQDw6NEjBAcHq13+7NmzSE5OBgCmViLKJ8T5xRmk+e+oWbOmXCXH0Y3qDR8+XO74kI0o+a/58uULzp8/DyAz3U29evUMXCL6Gu3du1d47O7uLjcnnJiVlRXGjx8vPD948KDQKz+rY8eOCb2xnJ2d0atXL5Wf/9tvvwnH+8OHD/H8+XOlyz1+/FgYwm9sbIzffvtN5Tp79+4NZ2dnAJmTYZ44cULlskS5VVD2d4lEgsOHDwvPx48fr7LHc6VKleTuH8XnCVXatm0rPPbw8NC4vK75+vri4MGDwvOBAwdi0qRJ2VqHo6Mj1q1bp3Z709enUqVKaNq0qfD8v3rdCWSOdJARH9P033PlyhUhMGJnZyfXkS4rMzMzTJw4UXi+d+9eZGRkKF328uXL+PjxI4DM1JmjR49Wud4xY8YIwcLQ0FCVDbyRkZG4cOGC8Fxc12bVpEkTYdRneno69u/fr/LzxYGqoUOHqpzjo0SJEnLbR5s6k75+QUFBch1XpkyZonYkybhx42BpaQkgsx5S1WZUEPd3cX2SF4HMPB3P1qVLFyF1i6enp9zJMCvZqBtTU1N07NgRfn5+2f68oKAgHD9+HHfu3MGHDx/w+fNnFClSBGXLlkWjRo3Qu3dvlTmLmzdvjtDQULnXZsyYIdfrS0abCa5jY2Nx6NAhnD9/Hu/fv0dSUhIcHBxQv359DB48OFsjhqKjo3HkyBHcuHEDwcHBiI2NReHChVGqVCk0bNgQ3bp1Q4UKFbReX2pqKg4ePIizZ8/i9evXSExMRIkSJVCjRg306NFD6GGmb1KpFBcvXoSHhwdevnyJyMhIFC1aFK6urujUqRM6deqUreBATEwMjh07hps3b+L169eIjo6GhYUFSpQogfr166Nr165a5R+VSqW4fPkyzp49i6dPnyIiIgJJSUmwsLCAnZ0dypQpg2rVquHHH3+Em5ubUEYfHx8MHDhQYX2qGpEuX76sEPHVFalUinPnzuHixYt4/PgxoqKiAAD29vaoUaMGWrVqhdatW6s88Sorc2hoqMLrup7QV9Vkwffu3cOxY8dw//59REREID4+HgMHDsSsWbMU1vHx40d4eHjg9u3bePfuHWJjY2FlZYVvvvkGDRs2RM+ePbWaA0EikeDMmTO4ePEi/P39ER0djZSUFFhYWKB48eJwcnJC9erV0axZM7l0Ax4eHgrnDWXbTkaWazq/cXBwECZk0zalRm62vXiyPpn169fL9WCScXd3x9KlS+VeS05Oxq1bt+Dt7Y1nz57h7du3+Pz5M8zMzFCsWDFUrlwZTZs2RefOnXU+4W6xYsVQrlw5ocdH1onslE1E+OnTJ3h4eODSpUv4+PEjoqOjUbhwYWGkACBfL2lzvggNDcWRI0dw+/ZtvH//Hp8/f0bRokVRpkwZNGrUCD169ECpUqXUrkN8HnNzcxMmWb5+/TqOHz8unBMTExMxY8YMDB48WPjbCxcuCBMONm/eXKvzt0Qigbe3N7y8vPDkyRO8efMGcXFxMDIygq2tLVxcXISya8pRqy1l21U2Aejt27eFdCKlS5dG8+bN0b9/f60nMxRLSkqCh4cHTp06JeyP9vb2qFOnDvr164c6depoXIchtk9+lpCQAC8vL+G5plRqrVu3xty5c5GYmIjY2FjcvXtX6RwfshHdsnWquyn55ptv0KBBA6Fh7OLFi6hSpYrCcpcvXxYef//992qPPSMjI3Tp0kXoxXbx4kW5Y8sQHj9+jIMHD+LevXsIDw+Hubk5nJyc0KpVK/Tr1y9bvZZlaZCvXr2Kp0+fIjo6GlKpFHZ2dqhZsybatm2Lli1bKt3uuqhTnz59itu3b+PBgwd49eoVoqOjIZFIULRoUTg5OaF+/fro1asXvvnmG62/U0FWUPZ3X19fYTRN4cKF0bp1a7Xfy93dXQjs3L59G4mJiQq9NcVatmyJuXPnQiqV4tSpU5g2bVqeTsouSxkCZPb4/PXXX3O8Lk1z40VFReHatWvw9fXFy5cv8eHDByQkJKBQoUIoXrw4atWqhXbt2gmdLNVZt26dcG0muydOSUnBsWPHcPr0abx58waxsbGws7NDgwYNMHz4cIX71ISEBHh6euLUqVMICQlBXFwcHB0d8eOPP2LEiBEoWbKk2jIoq8ffvn2LAwcO4ObNm/j48SMkEgmcnZ3Rrl07DBo0SCHI9/r1a/z777+4e/cuQkNDYWxsjG+//RadO3dG7969FXrhK2PIc0utWrWE4y46OhoJCQnCdYD4vCm7Zk5PT8e5c+dw6tQpBAQEICIiAikpKdiwYQNatmwJQPlvq45EIsGJEydw+fJl+Pv7IyoqCqampnBwcECdOnXQvn17/PDDDxq/i7Lf8927dzh69CiuX7+OsLAwxMbGwtXVVS5TS2JionA+K1y4sFZzeAGZbUY3b97EvXv3EBgYiE+fPiE1NRXW1tb45ptvULduXfTs2TNb7SvqKNuuiYmJwjEju0YsXrw4ateujV69eqlNM6mOl5cXDh06hMePH+PTp0+wsrJChQoV0LZtW/Tq1UurVNZ5vX105fHjx8Ljhg0barzfa9CgASwsLJCSkoKIiAg8ePAAdevWVVhOXGe2a9dObYq0QoUKoW3btkJddPHiRbRq1UphuStXrgiBIWdnZ9SuXVttWd3d3YV6+PLly3LzfMi8fftWrqHc3d1d7Tq7du0q1MMvX75ESEiIMBLdEGJiYnD48GFcuHAB79+/F9ooGzZsiD59+ii99lDn8ePHOHXqFHx8fBAeHo74+HjY2NigXLlyaNy4MXr16qVyHnVl15jK2vkAYMmSJQr3I7qsc/OS+BhycHDQuM1tbGxQq1Yt4d7s/PnzSs8LBXF/b9CgAaytrfHlyxdcvXpVaFfRlzwN1DRr1gw2NjaIi4vDiRMnMGHCBKUXwO/fvxcapxo1agR7e/tsfU5qaioWLlyII0eOID09Xe69mJgYxMTE4PHjx9ixYwd+++039O/fP+dfSgv379/HpEmTEB4eLvf6+/fv8f79e3h6euKPP/5Az549Na7ryJEjWLp0Kb58+SL3emxsLGJjY+Hv74/du3ejf//+mDZtmsaLyqCgIIwZM0aYd0QmJCQEISEhOHXqFHr37q30YNCl+Ph4TJ06Ve7GDsiMtkZGRuL27ds4cOAANmzYoNX+sHfvXvz5558K2yk1NRVfvnxBUFAQ9u/fj65du+KPP/5QWXFHRkZi7NixePjwocJ7SUlJCA0NRWhoKHx8fLBt2zbs3LnToBOQKhMcHIxJkyYp7fWYmJgo/M5Vq1bFX3/9ZdAKWRPZsS3ucahKRkYG1q1bh+3btwuNxTJxcXGIi4uDv78/9uzZg19++QUTJ05UeUP+5s0bjBkzRulQy8TERLx79w7v3r3DrVu3sHHjRly4cAH/+9//cvYl86nIyEjhsaZ5RnS57XPCz88PgwcPFnoIi0kkEiQmJiI0NBSXLl3Cpk2bsH79+mxf7Gkirrjj4+PVLnvp0iXMnDkTcXFxOvv8TZs2YdOmTQrbPyoqClFRUfDz88O2bdswduxYDB8+XOv1fvnyBTNmzMDFixc1Lnv16lXhsTYB/48fP6JLly6IjY1V+n54eDjCw8Nx8+ZNbNq0CatXr9bqhj+7Dh06hAULFiikJwgICEBAQAD279+PJUuWCEFkbbx69Qrjx49XOIeEhYXh9OnTOH36NMaMGSM34iOr/LJ98pOHDx8Kv5OVlZXGzhcWFhaoVauWkI7Q29tboSEnJSVFrnOQNo0j9evXF24gvL29MWHCBIVlfHx8sr1OGdn31HVQWVvr1q3Dxo0b5XqXJiUl4cmTJ3jy5An27t2Lv/76S6tJ6318fDB79mwhNYGY7Jrq9OnTqFmzJtauXat2Evic6N69uzDSIyvZ+fHhw4fYvn07JkyYgGHDhun08/ObgrS/i9dZq1YtjcdD9erVUahQISQlJSElJQWPHj1Se41ub2+PihUrCo3WT5480ck8H9oICQmRS8/Wp08fWFhY6OWz9uzZIzTUZ/Xlyxd8+fIFb968gYeHBxo0aIA1a9agWLFiWq8/JCQEY8eOxYsXL+ReDw8Px/Hjx3H27Fls3LhRaJB6/Pgxxo4dq3CfHBISgn379uHEiRPYvn07atasqXUZjh8/jrlz5yp0LHr58iVevnyJ8+fPY9euXUKj3MaNG7Fu3TqFHvR+fn7w8/PDuXPnsGXLFrUNsoY+t2RtYIyPj1fZYSM8PByTJk3C/fv3dfb5fn5++PXXXxXO7SkpKUhISBDSy/zwww9YuXKlQspCdQ4ePIhFixYpXNNm5eXlJWRkqV27tlZ15oQJE3Du3Dml78najZ49e4Y9e/Zg4MCBWrWvZNfr168xduxYhWvEDx8+4MOHDzh16hR69uyJP/74Q+vPTk1NxYIFC3Do0CGF1+/du4d79+7Bw8MD27ZtU/tb5Iftk1Pie1dtgqNmZmYoUaIEQkJCAGTuT8oCNTmp32SBGtlccOrWqWweVGXrlPnw4QPevn2r0PYg/ixnZ2eN11OOjo5wdnYWMh95e3sbrF3o4cOHGD9+vDD/pIysjfLo0aMYNWqUVnNoxcXF4ffffxeyPIjJ2hrv3r2LrVu3YsGCBWjTpo3Ovgeg/zpXn7J7DGVdztvbG2PGjFFYpiDu77I0s1evXoVEIsHt27f1OmozTwM15ubmaNu2LQ4cOIDQ0FDcvXtX6cnN09MTUqkUQObEPdmRmJiIn3/+WS6/r5OTE6pWrYqiRYsiLi4ODx48wKdPn5CcnIwFCxYgPj4eI0eOlFuPrDHEy8sLr1+/BpAZif/2228VPlPdRXxgYCBWrVqFxMRE2Nvbo27durC1tUV4eDi8vb2RnJwsTNDt4uKi9iJ0+/btWL58ufDc3Nwcbm5uKFWqFD5//gwfHx/ExsYiPT0du3fvxsePH7F27VqVDaChoaEYNGgQIiIihNcqVqyIKlWqwMjICM+fP0dAQAAOHDig9sJUF2bMmIHLly/DyMgI1atXR/ny5ZGamoqHDx8KPWoePnyIwYMHY//+/Wp7bi5atAh79uwRnhcrVgw1a9aEg4MDUlJS4O/vj4CAAEilUhw9ehSfPn3Cli1bFHp7p6enY/jw4Xj27JnwmouLCypWrAhra2ukpqYiIiICL168kNuGMo6OjujXrx8A+eF0stey0kcO3aCgIPTv318u37eLiwsqV64s9xsDwLNnz9C7d2/8+++/CqMcZGWW9XgDMnsqZU1LaGtrq/PvILZkyRIhSOPi4oJKlSrB1NQUwcHBcr9feno6Jk2aJFchOzo6onr16rCzs0NCQgIeP36Md+/eIS0tDX///Teio6OxYMEChc+Mj4/HkCFDhCHOxsbGqFy5MsqXLw8rKyskJycjPDwcL168QExMjMLfly9fHv369dO47fKzJ0+eCBetAJRetMroatu3bNkSFStWlEufUq1aNaXn2xo1asg9j4uLE4I09vb2qFChAkqWLIlChQohOTkZb9++xZMnT5CWlobQ0FD0798fx44d02lwTTyfk7pj++HDh1i/fj0kEglsbW1Rr149FCtWDFFRUfD398/RZ8+fP1/unGNlZYX69evDwcEBERER8PHxQWJiIlJSUrBq1SphEk1NpFIpfvvtN1y9ehVGRkb47rvvUKFCBUilUgQGBsrVNRkZGXIjHbQZLSIb5QBkNjhUqFAB33zzDaysrCCRSPD+/Xv4+fkhJSUFsbGxGD58OP755x+NvXCy4/Lly1i8eDGAzP22Tp06sLKyQnBwMB48eICMjAzExcVhwoQJ2LRpk1Y9nz59+oTBgwcjIiICRYsWRZ06deDg4ICYmBh4e3sLHQo2bNiAChUqCDlws8oP20eXPnz4gMOHD+P9+/dITk6GjY0NypQpg7p162p9MyBu1HBxcdFq4tMqVaoIgRrZ9Z3YmzdvhMY6IyMjrYK44mWUrTNrWbO7zvT0dLx580blqBF92rNnj9Dz93//+x+qV68OMzMzBAQE4OnTpwAyG/1++eUX/Pvvv6hcubLKdZ09exa//fabkEbV0tISNWrUQOnSpWFsbIzg4GA8evRImBy9V69eOHLkiFzngNzWqbK63NzcHBUrVoSTkxOsra0hlUoREREBPz8/xMTEQCKRCPm182uw5vPnzzh79ixevXqFL1++oEiRIihRogRq1qwJV1dXrTpAFKT9PbvrNDMzg4uLixCICgoK0tiZqk6dOsJ18Z07d/IsUJN1BLGqekAXPn36JDQYlS1bFuXLl4ednR3Mzc3x5csXBAQEIDAwEEBmw8WQIUNw6NAhrRq94+Pj8csvvyA4OBhFihRBvXr1hGsPb29vJCUlITU1FWPHjsXJkychkUgwZMgQxMfHo1ixYqhXrx5sbW3x4cMH+Pj4QCKRID4+HmPGjMG5c+dgbW2tsQw3btzAggULkJGRAWdnZ1SrVg0WFhZ4+fKlcD35/PlzTJ48Gdu3b8fmzZuFuRhdXV1RqVIlmJiY4MmTJ8J28PX1xZIlSzB//nyVn2voc0vWzj6qtlVqaipGjRqFZ8+ewdTUFLVq1ULZsmWRmpqqMpWhJnfv3sWwYcOEwJj4fl4ikcDPz08I4Ny+fRt9+vTB/v37tQrWnDt3TpijoESJEqhduzasra3x6dMnhe8sTvmm7l5FTPa7mZqaonz58nB2doa1tTVMTEwQFRWFJ0+eIDw8HFKpFLt370ZqaqrcBNi59eXLFwwbNgzv37+Xa9uJjY2Fj4+PcD9x6NAhpKSkyLUFqTNnzhwcO3YMxsbGqFGjBsqVKwepVIpHjx4JHXSfPXuGadOmYevWrSrXY+jtkxuy9sSckh3/Yl++fJFr98lu/SYbyZH13jC79ZujoyOKFy8uNKQHBQUp3MeK16lplKX4s2UN1+rmAtGnDx8+YOnSpYiLi4OVlRUaNGiA4sWL49OnT/Dx8UFSUhLS09Oxfv16ZGRkKO0sIhMREYFBgwbJfZeKFSvC1dUVhQsXRlRUFO7du4fY2Fh8/vwZEydOxPLly9GpUye59cjawi5evCgEj1q2bKk0GFC+fHm55/qsc/VNH8cQUHD39zp16ggdUe/cufP1BGqAzADIgQMHAGQGZJQFamS5iYsWLZqtHqsAMG/ePCFI4+zsjPnz5ytE6dLT03Hw4EEsWbIEqampWLt2LerXry/XE1DWq3X69OnCTUinTp00ptXIatmyZUhPT8f06dMxYMAAuUaEjx8/Yvjw4QgICEBGRgZWr14tF2AQe/DggdyknI0bN8aSJUvkbl5TU1OxZs0abN++HUBm2pldu3apzMc5a9YsoaKxtrbGihUr0KxZM7llrl+/jt9++w07d+7UamhsTjx8+BASiQRlypTBmjVrFHrEHj58GPPmzYNEIkFAQACWL1+u8kL5yJEjwjYsUqQIpk+fji5duiiU3dvbG1OnThV6H2/fvl3hYvnq1atCkMbBwQEbNmxQaBCWCQwMxPHjx+UqXWdnZ8yZMweAfKBG9pq+paamYvLkyUKQxt7eHitXrlS4Sb116xZ+/fVXxMTEIDIyElOmTMHBgwfltpmszLIRYEBmUCavvguQ2fN83759KFWqFFauXKlwAS7u/b5+/Xq5uTHmzJmDVq1aKTRanD17Fr///ju+fPmCQ4cOoWHDhgo3x0ePHhUuUitUqIB169YpDdhKpVI8efIEHh4echVrjRo1UKNGDYNuu9x4/PixXJrKVq1aCbnkldHVth80aBCAzJ7cshvrJk2aaNVzxsbGBiNHjkT79u1VppWMiorCsmXLcPz4cSQkJGDu3LlqJ47MjpiYGLlRiupSlK1btw7p6elC70rxcaduwklVzpw5I3e+6dq1K2bNmiV3boqPj8e8efOEunb37t2oW7euxgmIHz58iLS0NLi4uGDlypUKjWji8r5+/VoYSVSsWDGtesVbWlpiwIAB6NSpE7777julqdLi4+OxYcMG7NixA2lpaZgxYwbOnj2rszmzVqxYAWNjY0ydOhWDBg2SW++rV68wceJEBAYGQiKRYMaMGTh9+rTKYfIyGzZsQGpqKoYNG4YxY8bIdXyIjY3FhAkThF5Aq1evRtu2bZU2sOpj+xw/fjxHqWXVGThwoNpzhMy6detUvufm5oZx48Zp7KkoPs60De6IUzApa2QWv2Zvb69Vr3bxZ8fGxiI6OlquASoqKkoueKtNWS0tLWFnZyfU4a9fvzZIoGb58uWwsLDAwoULFW5cxSPGZSOjPTw8lF4vBgYGYvr06ZBIJDAyMsKQIUMwatQohbQBISEhmDZtGu7fv4+PHz9ixowZco1Iua1TW7VqhWbNmqF+/fpCHm2x9PR0HD9+HAsWLEBiYiL++usvtGnTRmUvOz8/P7nUO7rQpEkTNGnSRONyly9fVhiJLuPs7IxffvkF3bt3VxuwKUj7e06Pd9k5TlVQSUwcaBSn/NA3cZpTBwcHvabdc3Z2xu+//45WrVqprJtfvHiBWbNm4enTp/D398e2bdvUzsMgs2/fPqSmpqJnz56YNm2a3LVHWFgYhgwZgtevXyM5ORkbN25EQEAAEhISMG7cOAwfPlzu+jkwMBBDhgxBREQEIiMjsXv3bowdO1ZjGZYsWYJChQph8eLFCj2jz5w5g19//RXp6em4desWdu3ahb/++gslSpTAqlWrFOqcnTt3Cql1Dx8+jOHDh6u8ptP1uSW7xJ1U7ezsVKb5O3/+PNLS0uDm5oYlS5YofJ/sXnvGxcVhypQpQpDG2dkZq1atEiZmlzlx4gR+//13JCcnIzg4GDNnzsTff/+tcf1//vknzMzMMGfOHPTo0UPufJa1rOLrGW3ry/r162PIkCH48ccflXaskkqluHr1KmbNmoXo6Gjs378fHTp00DoQpMm+ffsgkUjwww8/YNmyZXKpdZOTk7Fs2TJh3oXjx4+jcePG6NChg9p1Pnr0CL6+vqhWrRqWLVsm13AslUqxZ88eoVPSjRs3cPfuXZXzSOp6+wQHB6ts78qpGjVqKO3cLa6XZPfy6kgkErkgjKrOPGLanKuzLvP69WuFTgA5rd9kDdevX79G8+bNdbJOcTkN4e+//4ZEIkHHjh3xxx9/yO13cXFxmD17tjC/yd9//40ff/xRaae0jIwMTJkyRWiAr169OubNm6cQGEhJScHWrVuxfv16SKVSzJ07Vwhgy8iuMWWp/4DM+x1tRoPoo85V12kgJ2xtbZVmdRAfQx8+fNBqXeJjLSYmRuEaESi4+3teXiPmeaCmVq1awhCj8+fPY86cOXIXMw8ePMDbt28BZE7Yk51h3/fu3RNu2pycnFT21DAxMUHfvn1haWmJGTNmID09HRs2bMC2bdty9+WUSE1Nxfz585VOzFmqVCmsWrUKnTp1glQqha+vLz59+oQSJUooLLt69WohElurVi1s2LBBIcpqbm6OqVOnIjU1VZhHYP369ejRo4dCxXr79m2ht7ORkRHWr1+vNDVNkyZNsHHjRvTv319uInldkkgksLKyws6dO+Hk5KTwfo8ePQBASL926NAh/PLLLwrLxsfHY9myZQAye9Ht2LFDZWClQYMG2LlzJ9zd3ZGSkoJt27ahf//+cg1o4uHgEyZMULkuIDMyn5tc0vpw8uRJIe2AmZkZtm3bpjRi3ahRI2zZsgV9+vRBWloanj17htOnT+e7ER/p6ekoVKgQdu7cqXReE9nx8P79eyHPt62tLfbt26d0vwIyzzHFihUTggLr169XaCQV7wezZs1SGqQB/r/3WF71vtSV69evK4wEysjIEHp4iCeQa9WqldCrTRldb/uckjXkqWNvb4/ly5cjJiYGN27cgJeXF4KCghR6weTEli1b5NJnqMuRnZaWhokTJ2LUqFEK72W3J01GRoZcQL9NmzZYvHixwjYtUqQIli9fjoSEBKGRb8WKFWjZsqXagEdaWhocHBywe/dupXWruLzieSG0mQMKyJwDRlOazSJFimDatGlITEzEgQMHEBwcjJs3b2rVqKkNiUSCKVOmKO3gUKFCBezcuRMdO3ZETEwMIiIisGvXLrU9uYDM64ARI0Zg8uTJCu/Z2tpi1apVaNWqlZCK8vHjx0r3X31sHy8vLxw7dkztOrOrdevWWgVq1PH19cWgQYMwevRotcFZcRo4bdPkihtBlKUbzMk6s6aDlM3HoGydypZXt15Zw7UuUyNmh0QiwZ9//qm0h3+dOnWwfft2dO3aFampqQgICMDx48fRvXt3hWUXLlwopKSZPn26yjl3ypYti23btqFHjx549eoVbty4AT8/P43ndG1p6ulrYmKCrl27wtLSEpMmTYJEIsGBAwdUTs4eFBSk80l3ixUrlutzWnBwMGbPno3Lly9j9erVKhttC9L+Ll6vtuvUdLxnJb4GyJq6S5/EDRuqrjN1RdnxmVWlSpWwa9cutG3bFhEREdi3bx9GjBihMaVRamoqOnXqpHSEesmSJbFw4UL07dsXAIS6Z+zYsUoDMBUrVsTUqVOFY+/MmTNaBWokEgk2b96sdPRUu3btcOfOHSEN0ZIlS2BpaYldu3Ypvf4bMmQIbty4gTt37iAjIwNnz55VOQpG1+eW7Hjx4oXcJOWarjtdXFywdetWpQGl7F577t69W0hbZ2Njg127dimdk6pTp04oVKiQ8BtevXpVbYBAXN4VK1YodBTIWlapVCp3z6LtcTRlyhS17xsZGaF58+b4+++/hTT1//77r84CNRKJBJUrV8amTZsU2r0sLS0xd+5cxMfHC52rVq9ejXbt2qm9Xk9NTYWzszN2796tkP7OyMgIgwYNwv3794WOdadOnVL5O+h6+4SHh+u8zkxMTFQaqKlatarQkcLb2xsSiURtx2NfX1/hOgVQrMsAyN0zFylSROkxlFWhQoVQuHBhJCQkAFCsi5KTk+U+Nzt1poyh6kx9kEgkaNKkCZYvX66wn9vY2ODPP//EkCFD4OvrK9z7KtunTpw4IaTYqlmzJnbv3q3097KwsMDYsWMhlUqxfv16JCYmYtu2bZg3b55Ovo8+6lxdH0OlS5dWGqgRB9xlmYQqVaqkcj1fvnxRmDIiLi5O7hqxIO/v4uuEV69eIS0tTatsDjmhmy6o2SQ7kcbHx8tNxgVACLSIl9PWzp07hcfTpk3TOJy2a9euQiV+69YtpWmLcsvFxUVpkEb8vmwEiVQqFdJIiAUFBeHu3bvC8zlz5qi9iJo8ebKQ1zA+Ph6nTp1SWEZ2gQpkNqqomz+gbt26aN++vcr3dWHw4MEqG3SBzGCNbAibVCqVK7/M0aNHhR58ffv21XhTX758eSEYERsbi5s3b8q9L55XIr/kicwO8TwuvXv3VjussHr16kJADAD279+v17LlVL9+/TQ2+u7Zs0cIao4ePVrtfgVkBu0aNWoEIPNYyzrsX7wfZCefckEhm19A/G///v3C5KLA/48oW79+vdo0iLre9nlBPNGcOGVCTqSmpmLTpk1ydVHFihXVzhNSokQJnaW+uHXrFt6/fw8gMzg7e/ZslYEvIyMjzJ07V7hheffunZAOSp3Ro0drdRzIygFA4yTAOdGtWzfhsTjFWm6VKVMGQ4cOVfm+g4ODXK7dI0eOaBwWbmdnpzQ/r0zx4sXlGmV10UNHX9snt2Qp8yZNmoS9e/fCy8sLz549w71793DkyBGMHTtWSKGZkZGB9evXC6OElRHPQ6XNzTIAuYYQ2U1zbteZdbms82Nl/ZycrFfZnFt5oW7dumrTMFWsWFEupauy67MXL14Io8aqVKkiBOhVsbKykutJePLkyewWO9dat24tBDfy0zEEZPYUHDp0KLZs2YLr16/jyZMnePToEc6dO4e5c+fKNVBevXoVU6ZMUZh7Q6Yg7e/i17TtyCdeTptjSNzbNTw8XGlOeX0QNxBoMzltcHAw5s+fr/ZfbkdLWltbC5PKR0REyE3Sq4qZmRmmTZum8v06derI9XQtXrw4RowYoXL5n376SbhOEY/UVad58+ZqU9xlvaft1auX2k464uVVzUGTHbo+t9y7dw8jRoyQ21c1nWN//fVXrY9LdaRSqdwcKKNHj1YapJFp1aoVGjduLDzX5n6zevXqSoM0WUVERMjNYaPra88aNWoI+4mu64Rp06apPafNmDFDaPsJDQ3V6np9ypQpKucoAuSvE3WxX+tz++RUs2bNhIb+yMhItSN50tLSsHbtWrnXdHWNmHXZrHVR1ufa1m/5oc7UByMjI8yePVtlMNLU1FSu49q9e/eUjoYQZ8qYN2+ext9r+PDhQv17+vRplddN+pKTOlffXF1d5UZdrlmzRu3yGzduVJgbLutxVJD3dwcHB2G/TEtLU5hbT5fyfEQNkBmAWbt2LaRSKTw9PYXhm6mpqTh79iyAzBEx2uS0l0lLSxMa2YoUKaKQwkuV+vXr4/Xr15BKpXjw4EG2U61pos1kVJUrVxYaZmTzsYiJJ0aqXLmyxjx+VlZW6NChgzCqxsfHB71795ZbRjyBkzYjJ9zd3ZUGfHRFmzJ06dJFSEUmLr/MjRs3hMeahgTLNGjQQAho3L9/Xy71j/gC7/Dhw2jWrFm+mRxPk/j4eLmgnzaR/B49eggXzE+ePEFiYqLKHpiGok3AUNyjrGPHjlqtt0GDBsIkrvfv35fLayneD/bv36+z3hUFSUREBMaNG4cOHTpg9uzZKlM96Xrb60JSUhIePXqEgIAAREdHIyEhQe7CS1zBajsnzJ49e+Tm4MnIyBBy3Irng5Kl3lDX661169Y664khriuaNGki10tEGUdHRzRq1EjIterj46NxzhVt8+aLJx/MydxVspzmL1++REREBBISEuQaIcQXfTmdy0eZDh06aPw9OnXqhCVLliA9PR2fPn3C69ev1TbyNGvWTOMFY5UqVYTrH2XXAVnpavssXbpUSOuSF6ZOnaq044O1tTWqVauGatWqoVevXhg1apRQh/3555/46aeflKaHETfKaJueVdzRRdnExLldJwC5nmKAYnqWnKw36zrzirbXZ7IAtbLrB3Hd0L59e61GToo7EOlywmuxFy9ewN/fH6GhoYiPj1f4nWTllKUoVnYu79q1a7bTIudGy5Yt0aVLF6VlKVeuHMqVK4fu3btj7ty58PDwAABcuXIFJ0+eVNoBriDt77ktqzbHkPj8lJaWhpiYGK17ZuaG+Jytzbyg2vRK/+677zR2WouKisKjR48QFBSEz58/IykpSa7zgfhewt/fX2M6qbp162rcXhUrVhRSqDRr1kxt50NLS0s4OTkhKCgIUqkUoaGhGsvQunVrte9n/XtNy4tT6Io7oaiji3OLmJ+fn0Kqm8TERPj7+yuM/Pr555/V/u42NjZCJ6ncCgoKElJFmZiYaNXJtkePHsI9e9a5mZTRtrNoVFSU8LhQoULZysoi8+bNGzx9+hTv3r0Tfjfx8SCbUzA2NhYfP35UG5TSVsmSJdV2mAUyO/w0adIEFy9eBKD5et3CwkJjW5i4PUmb605AN9unfv36cqPu9cnJyQnt27cXOnusXr0aZmZm6Nevn1ybTnR0NGbPno1Hjx7J/b2urhEB9XVR1s/RdlRbfqgz9aFWrVoaO3u6urqiSpUqQidPHx8fuU4qnz59Eu5/KlSooHYUiIyFhQVq1qyJGzduCJlFtPm77NBVnZtXx5CRkRFGjhwpBMauXr2KGTNmYObMmXLzoKWmpmLz5s3YsWOHwjq+pv3d1NQU1tbWQueayMhIlC5dWqvPyi6DBGpKly6NevXqwdfXF3fu3EFERAQcHBxw+fJlYUREdkfTvHz5UoiCmZqaYtGiRVr9nbgHQVhYWLY+Uxva5EcV3xQo6ykkbmQRz6OjTu3atYVATdZe6uHh4XKNidqkk6hZsyaMjIxyPaGUMsWKFdNqEu+aNWsKj/39/SGVSuVu9sXD7A4dOiQ3OksV8W+eNXdpmzZthEnKrl27hg4dOqBbt25o3LgxKlasqJMUTfry8uVLodHOyspKq/2wcuXKsLKyQmJiItLT0/HixYt8NQm1bFJYdWJiYoQJwczMzIQJkDUR91jIuh+0bdsWR48eBQAcOHAAz549g7u7Oxo1aqTTyecNZezYsUpTCyUmJiI0NBQ3btzAtm3bEB0djRMnTsDf3x979+5VCNboY9vnRmxsLNauXQtPT0+lPaKU0XZUZdaRoMo4OTlhxYoVGlPhZc3hnRs5rStkgRpNI5rKlCmjddBF3JsmOz3OkpOT8ffff+PAgQNa/x66HA2rzXazsbFBuXLlhH3X399fbaBG03kLkA9mqesxbOjtk1vajE4tUaIEtmzZgrZt2yIuLg4SiQS7du3C77//rrCsuCFG2/Ss4gYzZQ05uV0noLjPZ70JkUgkWjUiideri97POSG+9lLF1dVV7vrh5cuXcseS+PrMx8dHqzzX4utNXdYNQGbKpb///luoszSRSCT48uWLxvmo8oI2oy3Mzc2xaNEivHv3Tpj7ZNu2bUrvrQrS/m5hYSHULTkpqzbHUNZlsvYM1Rdxz/e8+MxXr15h5cqVuHHjhtajhpSlAcqqYsWKGpcR78MVKlTQuLz4uNNmRI2mOjfrMaSpzNn5fH2dW16/fq0xf76ZmZkw1486lSpV0lnHQ/F1Y7ly5bSq48X3lhEREQgPD1c7j6G2HbhyOtIBAK5du4a//vorWyP7Y2JidBKoqVGjhlZtCjVr1hQCNZo6KJUrV05jQ6W2152AYbdPbv3+++94/Pgx3r59i7S0NCxatAjbtm1D3bp1UaRIEXz8+BF3795FUlISTExM0LRpUyEttLIRSTmpMwH1dVHW+lHbeaK0qTNl9FVn6oM2152y5WT7ZNZjQhx0S05O1npOl3fv3gmPw8LCdBao0Vedmxd69OiBmzdvCp1UPTw8cP78ebi5uaFEiRKIjY3FvXv3hGD5Tz/9JMwhBEBhCo6Cvr9bWloKgRp9jjozSKAGyAzE+Pr6Ij09HSdPnsTQoUOFHJJGRkbZDtTIJnUCMnfqnOTt00ceRmWTrmUl7r2blpam8L44qKLtxEjiyF7WRpqsPb61SWNTpEgRWFtby00OqivafifxcqmpqUhISBC2b0JCglxjrLLUG5pk/W7ly5fHb7/9huXLl0MqleL169dYsWIFVqxYARsbG9SqVQv16tVDixYttJ6DIa+If/NSpUppdQFobGyMkiVLCjcC+alxD8i8sdLU0108AaBEIsnReSDrfvDjjz9iwIABQuDzyZMnQoC3ePHiqFOnDtzc3NCyZUu9pHgyFCsrK1SsWBEVK1ZEhw4d0KNHD4SHhyMwMBBLly7FkiVL5JbXx7bPqdDQUPTv31/rSe9ktA3oZGVsbIzChQvDwcEBVatWRYsWLdCyZUutenPoMq1iTuoK8XBmTce8vlP/xcXFYdCgQdkeIZPT300ZbW8qS5UqJQRqxNtdGXGPI1U0XQcA+WP75BV7e3v07dsXmzZtAiA/YlZMPGpD255/4h5Xym7Cc7LOrMtlHY2a9XOSk5O1argWr9dQI1y1OSaMjIzkrh+yHhPia3RVv6U6uqobpFIpZs6cKYw0yY6EhIR8EajRlrGxMcaOHSvMBRQQEICwsDCF65SCtL9bWVkJQQxlPZ2VES+nzTGkjw5p2hDvW9rs76p6pTdv3lxj7/ibN29i9OjR2Z40XpsgSXbrO13Vj2Ka7r2z3ktoKoM4qKHq8w1xbilUqBCKFi2KihUrws3NDV27dtU4khrQ7bVcTq47ixcvDgsLC+HYjImJURuoyUl5s3Mcr1u3TuvOZWK6urbKSTuILq47xfco6o4rQ2+f3LKxscH+/fsxceJEYQRXeHg4Tp8+Lbdc4cKFMX/+fERERAiBGmXbMSd1ZtZls9ZFWZ9rW79pU2dmd53ZrTP1IScTwau77nz//r1B24b1WefmlVWrVsHBwQF79+6FVCpFQkKC0NFTxsjICEOGDEG7du3kAjVZj6OCvr/n1XWiwQI1bdq0wcKFC5GUlARPT0907txZmCOkTp06SlNcqCMbapkb+shDrItRF+JInbY7kHjYfNaKUvw8O5HyQoUK6SVQo20ZsqYCEAdqdHEiU/b7Dx06FN999x02btwIb29v4cCMi4vDtWvXcO3aNaxYsQINGzbEjBkztBq5kheym0JB2bL55QJLRpv9RF/ngdmzZ6N+/frYsmWL3PwRkZGROH/+PM6fP4+FCxfip59+wvTp07W+wCgoHB0dMXbsWKFH+4kTJzB58mS5G8L8dA6eMmWKEKQpXLgwevTogUaNGsHZ2Rn29vawtLQU0kz4+Phg4MCBALSvePfs2YP69evrpKy67K2k67oiq+zWFzLa3sjMnz9fCEKYmZmhS5cuaNasGcqXLw8HBwdYWloKDSbv378XUpXq8oJJ2/OlePtq2m66Gn2ZH7ZPXvr++++FQM27d++Qmpqq0FNf3CNUnPZEHXFQWVnjWE7WKU71l3Udyp5HRkZq1TAnXq+hggTaHhPqziW5vUbTVd1w6NAhuYbUH3/8ER06dECVKlVQsmRJWFpayu1j4kbvvM5Vrgt169aFmZmZ0LMwKChIIVBTkPZ3W1tboYxZy6CKpuM9q6w399m5hs4N8XWjppETuREdHY1JkyYJDUalS5dG7969hXvvokWLwsLCQqi3xI202tQl2a3v9JGdwBBl0Pe5xd3dXWdpSvV13Znd+03ZsabpGkrbFGY5aaS7ffu2XBCiVq1a6Nq1K6pVq4aSJUuicOHCcr/bgAEDhMZ+XdUJOWkHyavrzvywfXTB3t4e//zzD65fv46TJ0/i0aNHiIyMhJGREUqXLo2mTZuib9+++Oabb7B69Wrh75R1VMmaCSclJUXjPpqUlCT3m2WtiywtLWFpaSncL2lbv2lTZypbVp3s1pn6oO0xoe5eLL+0S+i7zs0rZmZm+P3339GrVy8cOnQIPj4++PjxI1JSUlCiRAm4ubmhd+/eqFGjhpDSXvZ3WdOhFvT9Pa+CmQYL1BQpUgQtWrTAqVOn8PLlS6xcuVKI5muTDzsr8UZydXXFiRMndFVUgxN/N22HV4mHzWft2SZ+np2eAPoaiq9tGbJ+vvh7ZL049PX11Vnl4ubmBjc3N0RGRsLX1xcPHjzAgwcP4O/vL1yEeHl5oWfPntixY0e25lbSl5ymUFC33xQE4mOlSJEiOs1r36pVK7Rq1QofPnwQ9oP79+8LveqlUinOnz8PHx8fHDhwIN+NssotcT7rtLQ03L17V26+En1u++x48OCBkGbHysoKhw4dUptaI78FJHND13VFboiDeNqMzhP3bjM2Nsa2bdvU5uzW1++m7flSvH3z4lypr+1z/PjxXE84ndXAgQPh7Oyc6/Vk7RkcGxuLEiVKyL0mPs9qO4JOnEZLnM9a2WtRUVFa3YSLP9vW1lahB7C9vT2KFi0qdHb58OGD2nR5QOaNgLiHoLKy5oWkpCStRoerO5eIr9HWr1+PVq1a6a6A2SDOnT1u3DiMHTtW7fLaHEd+fn5CRgBdadKkCZo0aZLr9ZiZmcHW1la4EVV2Li5I+3u5cuUQFBSkUAZ1NB3vWYnLYGpqqtNRr+rUrVtXSLMbERGBDx8+6KXTz6FDh4QGrEqVKmHv3r1qj++v6RpJn/RxbikIxNedhr7fFDcGJiUlITk5WWOD7/bt24XH3bp1w6JFi9QGOfTxu+WkHSSv7tH1sX2Cg4OxZ88enZRPpkaNGlpl49Gmbg0MDBQeV6tWTeH9rPf3oaGhGuuWrPWVqvpN1hlLV/VbuXLlhFHM+qoz9UHbY0LdvZj4urN58+ZCx6+8pq86V9tUbtqytbXF+PHjNS7n4uIizFejijitvYuLi9JryoK6v0skErmBC/qcw9BggRogMyAjm6Be1gvFwsICbdq0yfa67O3thcfaRtAKCvENkLZ5usXD3rPeZIjXl5SUhJiYGI03IvHx8TqJTCuj7XcSL2dubi53Qi5atCjMzc2FaLW2vfeyo3jx4mjXrp3QOB0dHY2TJ09i48aNiI2NRXJyMubOnSvs04Yk/j3DwsIU5vNRJiMjQ27Onry6OdUl8XkgPj4eSUlJOu8N+c0336BLly5CQPnjx484evQotm3bhqSkJMTGxmLp0qXYvHmzTj/X0LI2mmZNrZEX214bXl5ewmN3d3eN+c+zmx4tP8tJXSGeGFeXx7w4pZo28795eXkJPYcaN26scWJVff1uHz9+1GpkZF6fK/W1fby8vHDs2LFcl0+sdevWOgnUZG30UdZrSdz4GxAQgLS0NI0pMsU51lVd6BsbGyMjIwNSqRT+/v4a82VrWqesrLIgsr+/v9qJgAHg2bNnwmMTExODBf8/fvyocQ4HqVSK8PBw4XnWY0J8IyPuvZaXPn78KMwbUbRoUYwYMULt8vHx8VqlvQgKCspRSg11ihUrppNADSB/HCmrkwvS/l6+fHlhjjht5kpIS0tDQECA3N9rIt6PHR0ddTaXhyZubm5yz0+fPo1hw4bp/HPE10ijRo3SGIT9mq6R9EVf55aCICfXnbKAsIyurqGKFy8u10s7LCxM7bVIenq6MPrD2NgYU6ZM0XivrI/jIScNinlx3amv7RMeHq7zOjMxMTHb0yYok5GRIZc5Q9m8ldbW1nBwcBCuZfz9/TU28IrrK0dHR6Xn3fLlywsN19rUb+Hh4XJtnsrqN/Fr2s4vJF5OmzpTH7Q9JtTdi4mvOw3ZNqyvOlfXx1Dp0qW1CtRo48GDB8JjVXO/FtT9PSIiQrgfNzU1VZu2M7eM9bZmLXz//fcKjX8tWrTQKq9mVpUrVxaGXkZFReHt27c6KWN+mDC+cuXKwmPxhKzqiA+QKlWqyL3n6Ogod2GlTW9aPz8/vQ2/i46Olpu4SxXxpGCVK1dW+G3Ek3aLv7++2NnZYdCgQdi4caPwWmBgIEJCQvT+2Zq4uroKN5cJCQlK81hn9eLFC6FngomJic4mT8tLJUqUkBumrO3xkhulSpXC2LFj5Xo23L59WyEPaX44l+RG1t4tstRhMvra9tndbuKctNpM4n737t1slym/ykldIV4ua12RG+Jgx5s3bzQun19+N3E9o8rnz5/lUtPocrupkl+2T14SXzxbWVkpvbmpVauWcO2XmJiIp0+fql1namqq3G+sLOBlYWGBGjVqCM9lDRXqiLe3qiCaOF2ij49PttYp/p55TZtjIiAgQOgFqOz6QR/XZ7mpG7799luNc4jdv38/X6WdyImQkBC5tHNZR6QBBWt/F6/z0aNHGvO9P3nyRAhUWVhYaDVBsWzEDoA8vQ4uU6aM3MjlAwcOaJ2+KTuyU5ekp6fnyf1UQfdfPLfIiK9/Xr9+rdXk1+J9ysHBQWcNXUZGRnL7tKZrz5iYGCEtpL29vVyHM2VevXqll/lbxYEBdcR1cV5cd+aX7ZOXfHx8hMZgW1tbNG3aVOlyuanftKkzs1sPf/PNN/jf//6ndp1v3ryRO1cpEx4eLgSd1ZVV37Qd6a/umBBf1/j7++t10nd1/mt1bkJCgtxclKoCqAV1fxdfI1aoUEFj58DcMGigxsTEBB07dpR7LSdpz4DMXHfijbtv377cFE0gvlHQZgJDfRB/r+fPn+PFixdql09KSsKZM2eU/r2MeEfWJmWDp6enFiXNOW3KIF5G2fwQ4sp0//79eXYRXKdOHY05EcVD/mQXPfpUpEgRfPfdd8JzbXpMHzlyRHhcvXp1g00gl1vi/UBX5wFtNG/eXHgskUgUblbyeh/QNXFvVwBKb6z0se2zew4WB5A0DZ0ODw8XJoz8GojP9devX9c430B4eLgwN1zWv8+tcuXKCZ0uYmNj5XopKyP+3TSlz0hKStJ5qiGZ06dPa8xJfPLkSWEZBweHPEkNoK/ts3TpUrx8+VKn/3Q1f5MsDRCg2NtcpnDhwmjYsKHwXNNEzhcuXBACCra2tqhXr57S5Vq2bKn1Oj9+/CjXY078t2KyOYOAzB52mkaaiT9X1TrzgjaphMXXiNWqVVO4fmjWrJnw+OLFizrp3ZjdOlUc2NEmRc/+/fu1KkfXrl11fgyNGzdOq8/WRHxdZ21tLRfMFyso+7ubm5tQr8THx+PixYtq1ym+9v3++++1uq4V32OJA4x5QTwS4/3791i5cqXOPyM710iXLl0y2Ai4gkRf55aCQDZHHpDZyKhNfSE+L+nqekFGfMxqai/JzrEA6O93+/jxo8bG/ujoaFy/fl14ruvtpoy+tk/9+vV1Xmfqav6mtWvXCo/d3d1VpgEV11Fnz55Vu32Sk5Nx9uxZpX8r1rx5c2Gbv3nzRmMnGXH9Jq5vxZydneUyS2hqzxO/7+Liku05w3XlwYMHGjs+BwYGyrVNZL1PKFu2rDBCQiKRyJ13ckO8T+i6XSI7da6uj6ErV65o9bmabNmyRagHq1atqvI6qqDu73l5jWjQQA2QOQTsyJEjwj9xb6LsEg8R//fff3Hnzh2t/1bVQSFugNfU0KQv5cuXl2tMWLBggdqb0jVr1ggNdEWKFEGHDh0UlunRo4fw+OzZs2p7396/f1/v6bx27typ9oTs4eGBJ0+eAMi8IO7evbvCMr1790bRokUBZDYqiye/0yQ6OlqhcU6cp1qdz58/y+WTVNbjxBD7Ua9evYTHe/fuVXvB+vTpUxw8eFB43rt3b72WTZ+GDh0qjCa6ePGixkYHMWXnAW33A3EjhLGxscJkukWLFhUqJHEvpYJi165dwmMjIyOljfq63vaA/FBmbY4dcSWrLgiTnp6OOXPmFLjfQZ1GjRoJKcdSU1OxePFilctKpVIsXLhQ+P5OTk74/vvvdVYWY2NjuX1E05xF4t/txo0baoMlS5cu1dsw9nfv3snt61lFRkZiw4YNwvPu3bvnyWi5/LJ9ciM7ud137twp16usU6dOKpft27ev8PjYsWNy+cXFkpKS5G7Ce/bsqbInlLu7u9Co++bNGxw+fFjl569cuVL4PWrVqoWqVasqXa569epCvvP09HS1jbAHDx4UenkVLlxYJyk9csrX1xfnzp1T+X7W1F/Krs+qV68u3EQnJydj6tSpGkdDyKSmpipNE5TdOrVMmTLCsapp9POZM2dw9epVrcqXl7JzDD148AA7d+4Unrdr167A7+9mZmZy9y9r165V2fAREBAgdw3Sr18/lZ8vJq6rdFknakM2Ga/Mnj17sGbNGp1+hrguUdcwEx0djSVLluj0s79WX8O5JaeMjIzQs2dP4fmGDRvUXqtfvnwZ165dE57r+n5TfMxquu60tbUVAr9fvnxR26v7/v37eg2wLVu2TG2duHz5cmGEXenSpfHDDz/orSwy+Wn75IV169YJ150ODg4YNWqUymVbtGiBkiVLAshsB1I3/8nGjRuFOS1Kly6tcpRO8eLF5ebvW7FihcpOx7du3RImbDcxMVF7HImvkbdv367y/iAiIkJuri1t60x9kEqlWLRokcrvn56ejoULFwrP69SpozRtlbhteM2aNVplmJHRVdvwf6nOvXXrljCvlbGxMWbNmqVy2YK6v+flNaLBAzVFixZFtWrVhH+5yQXs5uYGd3d3AJkRzuHDh2Pz5s0qb2xSUlJw6dIljBo1SuXJWDxE7fLly1rfWOra5MmThW1z7949jBs3TqG3dGpqKlatWiXXyDR27FilE8798MMPQm8MqVSKMWPGyPXUkLl16xZGjx6NjIwMjUO5c8rMzAwJCQkYOnSoQq99ILNX7Zw5c4Tn3bt3VzrczdraGjNmzBCer1+/HtOmTVOZ61EqleL+/fv4448/0KxZM4WbvYkTJ2LEiBE4d+6cyh5S4eHhmDJlitBA4OzsDCcnJ4XlxPnd1TV46FLHjh2FtA0SiQS//PILvL29FZa7c+cOhg0bJvQKqFq1Ktq3b58nZdQHJycnueN55syZWLZsmcqAS1paGm7duoXffvtNOH+I9e7dG1OmTMH169dVHv9v3rzBtGnThOcNGzZUSNthbm4u7LcSiUTIs66Jh4cHXF1dhX/iOUXywufPnzFnzhy5G8sOHToonTxN19sekD92bt26pXGurCZNmgg3zL6+vli2bJnCsR0REYFx48bh2rVrBXbkmDKyHNIyp06dwuzZsxXqwPj4eMyYMQMXLlwQXvvtt98U0tnllrgXvbJzj1iDBg2E+RPevn2LadOmyU3WB2SW+/fff8eBAwf09ruZmZlh5cqV2L17NzIyMuTeCwoKwpAhQ4S6t3jx4hg8eLBeypFVftk+ubFw4UKMHz8eN27cUNmoHhkZiT/++EOud2TNmjWFueGUadq0KerWrQsg8zpoxIgRCh0TYmJiMGbMGCEtrq2trdr5H+zt7eV+24ULF8qNVAYyz+MrV66U68gyefJklesEIHd8njx5EitXrlTYFmfOnJELsg4dOlRhsnYxfdcRZmZmmDZtmtIOOw8fPsTPP/8sNCBVrFhRZSP777//LuyXt2/fRv/+/dWmt3jz5g02bNiA5s2bK00Fkd061c7OTkh9lZGRgfHjx8ulMJS9vnfvXkydOhUmJiYqe9Mayvnz59G9e3d4enqqrAtTUlKwZ88eDBkyRPhdihYtqnZy84K0vw8fPlzolBUcHIzRo0crpNt58eIFRo4cKXxW/fr1Nc6RA2SmzpYFeh0cHORGpmf1/v17ueMuOx1T1Jk1axZq164tPN+0aRN69uyJa9euqb0HDQoKwpw5czSOXBLXy5s3b1Y6+vLZs2fo378/Pn78mC/rkvzmazi35MagQYOEUfaxsbEYNGiQMPeA2OnTp+XOCc2aNVM5qjWnGjZsCEtLSwCZwWp1x4yxsbHcXGDTp09XmobszJkzGD58ONLT0/VyPJiZmeHZs2cYPXq0QqNiSkoKFi5cKNebfOLEiTq/Xlcmv2yf3Hrx4gUWL14sN1+ZWEREBGbMmCF08DU2Nsa8efPUznVsbm4uN/J1y5Yt2LNnj9x9Q0ZGBvbs2YOtW7cKr40fP15tGtsJEyYI7W337t3DtGnTFFJ2eXt7yx1HnTt3Vjsfa8+ePYW2qdjYWAwbNkxhntnQ0FAMHz5cyAbi7OystNONmLj+W7dundpls8vMzAxXr17F9OnT5dK3AkBcXBwmT54s3FcaGRmpvBbp1KmT0GkwISEBffv2xYEDB1SeF+Lj43HixAkMGDAACxYsULqMuG34/PnzGjP4fC117q+//govLy+lHQWTk5OxZcsWjB49WrjuGjx4MOrUqaN2nQVpfwcy263u3bsHIHMf1XfAXH9J1Qxk/vz5iIiIwK1btyCRSLB69Wps2rQJ1atXxzfffANzc3N8/vwZ7969Q2BgoHCgquoR1rhxY2FiOn9/f7Rr1w5ubm4oWrSo0Bj4ww8/5GokkDZq166NKVOmYPny5QCAq1evomnTpqhfvz5KlSqFuLg4+Pj4yKVbatWqldpGpEWLFqF3796IjIxEXFwchg8fDhcXF1SpUgVGRkZ4/vy5EHkeMmQILly4oLCj60KtWrVgY2ODixcvolu3bqhZsya+/fZbIZe8uGdS+fLl5RrEs+ratStCQkKEeWM8PT1x8uRJVKpUCd9++y2srKyQmJiI8PBw+Pv7q230lUqluHbtGq5duwYzMzNUrFgRzs7OsLa2RkJCAj58+IBHjx4JlbKJiYnKyHHr1q2FSPDKlStx48YNVKxYUa6yHjlypNqLguwyNzfH6tWr0b9/f0RHRyMiIgKDBg1CpUqVhPQX/v7+cg1a9vb2WLVqld6Ccnll7NixCA0NxbFjxyCVSrFjxw78888/+O677+Dk5ARLS0skJCQgNDQUL1++FCqFrKNggMyT8qlTp3Dq1ClYWlrC1dUVZcuWReHChfH582eEhITIzYtgaWmJqVOnKi1X69at8ffffwPIbBg/duwYnJyc5La3uv1bH65fv640p3BSUhJCQ0Ph5+cnF+hwdnaWC4hmpcttD2T2yi1VqhQ+fvyIiIgItG3bFj/88AOKFSsmnIOrVasmNOSWL18enTt3Foaz7tixAydPnkS1atVgb2+P0NBQ3L17FxKJBIULF8bUqVMxd+7cnGy6fKldu3a4d++e0MP98OHDOHPmDOrXr4/ixYsjKioKXl5echdCgwYNwk8//aTzsvz000+YN28eUlJScOXKFfzxxx8qby5tbGwwdOhQYbTKyZMncfPmTVSvXh2Ojo6IiIiAr68vEhMTYWpqirlz5+rlWPntt9+wePFiLF68GDt27ECdOnVgZWWF4OBg3L9/Xzjfm5qaYvHixSr3W13LL9snN6RSKc6fP4/z58/DysoKLi4uKFOmDAoXLoyUlBS8ffsWT58+lWvIdXJywoYNGzSOWlq1ahW6d++OiIgIhIaGokuXLqhXrx6cnJwQHR0NLy8vocOFqakp1qxZIzT2qjJ69Gg8ePAA3t7eSE5OxqRJk7Bp0yZUrVoVKSkpuHv3rlyPu3HjxqlM0SbTsGFDjBo1Suh9uXXrVhw/fhx169aFhYUFnj17JteY8MMPP2DkyJFq16lvsmNiypQpWLduHapXrw5TU1MEBgYKI52BzHmEli5dqrIRwsXFBatXr8akSZOQlJQEPz8/4YaqSpUqsLGxQWpqKqKiovDy5Uuteipmt06dMGEChg4dioyMDDx//hydOnVCrVq1ULZsWSQmJuLevXvCbzpp0iQcOnRIL9e9ufHkyRNMmzYNpqam+Pbbb1GuXDnY2NggPT0d4eHhePTokVzDhqWlJTZu3Kh0fhqxgrK/FytWDKtXr8bIkSORlpaG27dvo1mzZmjYsCHs7Ozw7t073L17V2g8cXR0xIoVK9SuU+bSpUvC37Vv3z5PGkOzMjc3x86dOzFz5kycPn0aQGa+/hEjRqBQoUKoVq0aHBwcYG1tjdTUVERHRyMwMFBhP5UdV1m5u7tjx44dCA4ORmpqKqZOnYrNmzejUqVKsLCwQEBAgHBNW6lSJTRq1Ajbtm3T/xcv4L6Gc0tO2djYYNWqVRg2bBiSkpLw5s0buLu7o0aNGihfvjwkEgn8/Pzk5g92dnZWO+o7p6ysrNCyZUucOnUKCQkJ8PLykgs2ZDVq1ChcunQJycnJCA0NRc+ePVGzZk2UK1dOaIeQdX7o2bMngoODtZpPITv69OmDy5cv4+bNm2jevDnc3NxQqlQpxMbGwsfHR25EaYcOHdSOMNa1/LB9cis5ORm7d+/G7t27Ubp0aVSqVAn29vZITk5GSEgI/Pz8hGt7Y2NjLF68WGVqJbHu3bvD19cXx48fR0ZGBhYtWoR//vlHmBvFz89Pbg7mrl27apzioXz58pg7dy5mz54NIDPt/7Vr19CgQQMULlwYQUFBch1cXF1d1Y5aADIblNetW4c+ffogMTERz58/R+vWrdGgQQM4OjoiLCwMPj4+wrV3kSJFsG7dOr3OvaHJiBEjsGfPHnh6euLixYto0KAB7O3tERERAR8fH7l72BEjRgidtbIyMTHBmjVrMHToUDx//hzx8fGYO3cuVqxYgZo1a8LR0REmJiaIi4vDmzdv8Pr1a6HjcuvWrZWus1WrVli9erXQTig714s7xrdr104YUfy11Lnnz5/HyZMnYWtri6pVqwojysLDw3H//n25Tu09evRQ2RYmVtD2d29vb6HtuGnTphrvI3PrqwvUmJubY8uWLVi/fj127tyJpKQkJCUlqc39aWZmpnKCSWtra0yfPh3z5s2DVCpFSEiIwpBmKysrvQdqAODnn39G0aJFsXTpUsTHxyM1NVVufgEZExMT9OvXD9OnT1fbuFG2bFns2rULY8eOFVIOBAQEKPQ46NmzJ6ZMmSLX+1rXli5dirS0NFy9ehUPHz5UOhF2jRo1sGHDBmEYrioTJkxAxYoVsWTJEnz69Anp6el49uyZ0tE6MtWrV1cITohPuBKJBM+fP5eb3FjM3t4e8+fPR+PGjZW+7+7ujhMnTgg3jz4+Pgr7ZL9+/XQaqAEyT4D79u3D5MmThbK/ePFCaRq0qlWrYs2aNUpHBBU0RkZGWLp0KapWrYp169YhLi4OEolE5b4l+xtxL0YZ8X6QnJwMPz8/lb2Ay5QpgxUrVqicgPaXX37BhQsX8Pr1a0gkEqWj2LI2rmbtqZGbUYfKPHnyRK6xTZ3mzZtj/vz5aieU1OW2BzIvmufOnYtx48ZBIpEgIiJCIeeou7u7XI/7P/74A5GRkUJwNCIiQmG4ccmSJbF69WqDzT2mT3PmzEHx4sWxadMmpKamIiEhQelwawsLC4wZM0YuL74uWVtbo3Xr1jhx4gQiIiJw9+5dtXm1x4wZg9DQUOH3jY2NlZuQEMjsGb5kyRK9TfLcokULmJubY9GiRQgLCxMayrKWYfHixWpv/vUhP2wfXUlMTMSjR49U5iQ2NjZG+/btMWfOHK0uhEuWLIndu3djypQp8Pf3h1Qqha+vr0KDgZ2dHZYsWSI3r40qZmZmWL9+PX7//Xchv7iyayQzMzOMHTtW64DKhAkTYG5ujo0bN0IikeDTp08KoxeAzIbi+fPna7x50HcdMWjQIMTGxmLTpk0IDg6Wm3hTpkSJElizZo3aEQhAZs/CAwcOYObMmcI12bt37+QaM7IqXbq0cEOYVXbr1IYNG2LOnDlYuHAh0tLSIJFIFPYTY2NjjBo1CiNGjMChQ4fUfh9DSktLU7o/ilWvXh1Lly5VmhIkq4KyvwPAjz/+iHXr1mHmzJmIiYlBUlKS0jquSpUqWLVqldaTlYtHvHft2lXtslmPO10GdSwtLbF69Wq0bNkSGzZswKtXrwBkdqDR1Ajq7OyMPn36oG/fvkqDpubm5vj7778xbNgw4X42KChIboJcILOD4Jo1a/L1MZCffE3nlpyoV68edu3ahV9//RUhISGQSqUq6/jvv/8eq1atUjtyLje6d+8ujPw7e/as2mu1ChUqYNWqVfj111+RlJQEqVSq9H6lV69emD17Nn7++Wedl7do0aLYunUrxowZgzdv3iht2wGAbt26Yf78+Tr/fHXyw/bRpdDQUJUBUmdnZ/zxxx9aXR/KLFy4ENbW1ti7dy+kUqnS6xkjIyP0799f685TsvSeixcvRmJiIuLi4nD+/HmF5Ro2bIjly5ejSJEiGtdZqVIl7NixA7/++ivev38PiUSidD8rW7YsVq5cqXHSe33Wf0Dmdd/mzZsxfvx4REREKE1lbmJigmHDhmHSpElq11WsWDHs378fS5YswZEjR5CWlob4+HihjUAZS0tLlZ34y5UrJ2RtApRfJ1WsWFEI1HxtdW5sbCxu376t9D1ra2tMmjQJffv21ToteEHY32XE14jdunXT6m9y46sL1ACZB+6ECRMwYMAAeHp64s6dOwgKCkJMTAzS0tJQuHBhlC5dGi4uLqhfvz6aNGmi9mKhT58+cHFxwcGDB+Hn54dPnz4JlVVe69GjB1q0aIHDhw/jxo0bCA4ORlxcHAoXLoySJUvi+++/R7du3dQOCROrWLEiTpw4gYMHD+LMmTN48+YNkpKS4ODggGrVqqFHjx55kge1SJEi2LRpE86dOwdPT0+8fPkSkZGRKFq0KFxdXdGxY0d06dJF64qgXbt2aNmyJU6fPo1bt27hyZMniI6ORmJiIgoVKgRHR0eUL18ederUQZMmTVCuXDmFdWzatAnPnz+Hl5cXHj9+jKCgIISFhSEpKQnm5uaws7ODi4sLmjRpgo4dO6o9cZiZmWHnzp04cuQILly4gMDAQMTGxubJ/BjlypXD0aNHce7cOVy4cAGPHz8WUlHZ2dmhRo0aaN26NVq3bp0ncy3kpQEDBsDd3R3Hjx/HnTt38OLFC0RHRyM1NRWFCxeGo6MjKlasCDc3NzRp0gSlSpVSWIenpycePXoEHx8fPH78GG/evMGnT5+QnJwMS0tLODg4oFKlSmjevDnatWundkiztbU1jhw5gn379uH69esICgrCly9f1O4H4nyq9erVU1pGfTA3N4e1tTWcnJxQs2ZNdOjQQWMjnJgutr1Ms2bNcPToUezduxcPHjzAhw8fkJiYqPIcXKhQIWzduhUnT56Ep6cnnj9/joSEBNja2qJs2bJo3bo13N3dYWNjo3ECz4Jq9OjR6Ny5Mw4fPoxbt27h/fv3+PLlC6ytrVG2bFk0atQIPXr0wDfffKPXcgwaNEiYXPbQoUNqAzUmJiZYtmwZ2rRpg4MHD+Lx48f4/PkzihYtilKlSqFFixbo1q0bHB0d9ZoCsE+fPqhbty4OHDiAO3fuCKlkypQpg2bNmqF///4ae6frQ37ZPjk1c+ZMtG3bFo8ePcLjx48RHh6O2NhYxMbGwtTUFEWLFkX58uVRu3ZtdO7cOdudBsqXL49Dhw7hzJkzOHXqFF69eiVcR5QtWxatWrVC165ds9U4ZG1tjTVr1qBnz544duwYHj16hIiICJiamqJUqVJo1KgRunfvrlVDuIyRkRFGjx6N1q1b4/Dhw7h9+zY+fvyItLQ0ODg4oGbNmnB3d9c693Fe1BETJkxAkyZNcPDgQdy/fx+fPn2CqakpnJyc8NNPP6Ffv34aO9HIVKpUCR4eHrh16xYuXbqEBw8e4NOnT/jy5QvMzc1RrFgxlCtXDjVq1ECjRo1Qq1YtldcmOalT+/Tpg9q1a2PXrl3w8fHBp0+fYGlpCUdHRzRo0ADdunVTOhIhP+jQoQOcnZ3x8OFDobduTEwMYmNjkZGRAWtra5QpU0a4rlPVy1SVgrC/yzRv3hxnzpzB0aNHcenSJYSEhODz588oXrw4KlSogA4dOqB9+/ZajxAPCQmBl5cXgMwGAVdXV7XLi487a2trufQmutKuXTu0adMGvr6+8PLywt27d4XzZkpKCgoXLgxbW1t8++23qFatGr7//nuVHQ/FypUrB09PT+zduxcXLlzAmzdvIJFI4ODgABcXF3To0AFt27bVedD3a1eQzy26ULNmTZw5cwYnTpzApUuX8OLFC0RFRcHU1BQODg6oU6cO2rdvr/fOrQ0bNoSLiwsCAgJw7tw5zJo1S2391LJlS5w8eRK7du3CrVu38PHjR5iYmKBEiRKoXbs2unbtqvMUbVmVL18eR44cwdGjR3H27Fm8e/dOOJ/Vrl0bPXv2VDo3aF7ID9snN6pUqYKtW7fCy8sLDx8+xKdPnxAVFQUTExPhHr5169Zo2bKl2nt4ZczNzfH777+jc+fOOHLkCHx9fYXRwI6OjnBzc0P37t2zPem4rP3tyJEjuHr1qnDf6+DggKpVq6JTp05o2bJlttptatWqhRMnTsDT0xPnzp3DmzdvEBsbC1tbW5QrVw5t2rRBly5dlE6ZkJW4/jM1NdVLyvzatWsLbZQXL15EaGgoEhMTUaJECTRo0AB9+/ZVGUzJytLSEvPmzcOwYcNw4sQJeHt7Izg4WO7aqWzZsqhUqRIaNGiAxo0bq23Xmzx5MurUqYOjR4/i2bNniIqKUjlNAvB11Ll79+7FnTt34Ovri/fv3yMqKgoSiQTFixfH//73P7Ro0QLt2rXLUQA+v+/vQGbqPFnnTWdnZ5VzTemSkdQQ0QYiItJKp06dhAuivXv3ZrvhhcjQhg4ditu3b8Pc3BxXrlyBg4ODoYskp3nz5kIPu8uXL6NMmTIGLhGR9lhHEOXeihUrhHQjO3bs0NhJbeHChfjnn38AZAYyR48erfcyEpF2Tp48iV9//RUAMGPGjDybT1Bb69atE+ZEGTt2rNx8J0T53a5du4SJ77t3745FixYZuERE+rVv3z7MmzcPALBgwQL07NlT75+Z98l3iYhIK9HR0cJw2saNG7MBjgqkCRMmAMic6H337t0GLg3R14N1BFHuffnyBQcOHAAAuLm5aZVJQDYa197eHoMGDdJr+Ygoe9q3b4+KFSsCyGxUzosMFkT/Fd7e3gAyRxSNHTvWwKUh0q/09HTs2LEDQOb8f5pS4+oKAzVERPmUj48PpFIpjIyMNOZgJcqvatSoIcwhtG/fPiH1IhHlDusIotzbvXs34uPjYWxsjN9++03j8lFRUQgMDAQADB8+XOvUGUSUN4yNjYXJrD9+/IijR48auEREX4f09HTcvXsXANC7d+88S8lOZCgnT54U5hf69ddftZpLURcYqCEiyqdkPVZat279Vee1pq/ftGnTYGVlhYSEBGzcuNHQxSH6KrCOIMqd6Ohooadkt27dtJpLQBYgLVWqFPr27avvIhJRDjRu3BgtWrQAAKxfvx6JiYkGLhFRwff06VPEx8fDysoKI0eONHRxiPQqNTUVa9euBQB8//33aN26dZ59NueoISIiov8szlFDRERERHmBc9QQEZE6eTNuh4g08vPzw/Hjx3O9njlz5uigNDkTHByMPXv25Ho948ePh62tbe4LRERERERERERERJTPMVBDlE8EBQVh7969uV6PIQM14eHhOvkOQ4cOZaCGiIiIiIiIiIiI/hMYqCEiIqL/rCtXrhi6CERERET0HzBu3DimOyMiIpU4Rw0REREREREREREREZGBGBu6AERERERERERERERERP9VDNQQEREREREREREREREZCAM1REREREREREREREREBsJADRERERERERERERERkYEwUENERERERERERERERGQgDNQQEREREREREREREREZCAM1REREREREREREREREBsJADRERERERERERERERkYEwUENERERERERERERERGQgDNQQEREREREREREREREZCAM1REREREREREREREREBsJADRERERERERERERERkYEwUENERERERERERERERGQgDNQQEREREREREREREREZCAM1REREREREREREREREBsJADRERERERERERERERkYEwUENEREREueLh4QFXV1e4urri/fv3hi6OTjVv3hyurq6YPn26wnvv378XvreHh4fKdXz48AFz5sxBy5YtUa1aNeFvLl26pM+iExERERERUQFhaugCEBEREVH2+fj4YODAgUrfs7S0hK2tLSpVqoRWrVqhU6dOMDc3z+MSZo+rqysAwM3NDf/884/G5cXff+zYsRg3bpxey5dTHz58QNeuXRETE2OwMvj6+mLAgAHC8/3796N27dp6/UwPDw/MmDEjV+vQdl8oaAYMGABfX1+F142NjWFtbY0yZcqgdu3a6NWrFypWrKh2XevWrcP69esVXjcyMoKVlRUcHR1Rs2ZNdO3aFfXq1RPeDw8PR9OmTZGRkYG6deti79692foOvXv3xsOHD2FqaoqbN2/Czs4uW39vSBkZGXj9+jUeP36Mx48f48mTJ3j58iUkEgkAYM+ePahfv75OPzM6Ohr//PMPLl26hNDQUABA6dKl0bJlSwwcOBDFihXTaj0BAQH4999/cefOHXz69AlWVlb49ttv0bFjR/To0QOmpry9JyIiIiqoeCVHRERE9JVJTk5GWFgYwsLCcO3aNezatQt///03ypQpY+ii/eds2rQJMTExMDU1xcSJE1GvXj1YWVkBAL755hu8f/8eLVq0AAAsWbIEXbt21XkZjh07Jvfc09NT74Eayr6MjAzExcUhLi4Oz549w759+zBx4kQMHz482+uSSqVISEjA69ev8fr1a3h4eKBr165YuHAhTExM4OjoiAYNGuDOnTu4f/8+QkNDUbp0aa3W/fbtWzx8+BAA8OOPPxaoIA0AHD9+XOkIOX3x8/PDmDFjEBERIfd6QEAAAgICcPjwYWzcuBHVq1dXu55Dhw5h/vz5QkAJAFJSUnD//n3cv38fHh4e2Lx5c4H7PYiIiIgoEwM1RERERAVcnz590LdvX+F5VFQUAgMDsX37doSFhSEwMBCjRo2Cp6cnTExMDFjSr0uZMmXw8uVLtcvcuXMHANCiRQsMGzZM4f3Y2Fh9FE2QnJyM8+fPAwCsrKyQmJiIc+fOYfbs2XodZdWyZUt89913St978uQJZs6cCUBx3xUrVKiQ3sqXX5w8eVJ4LJFIEBISgkuXLuHkyZNIT0/HqlWrULZsWbRt21bjuhYvXoxq1aoByAzUxMbGwsvLC7t370ZiYiI8PDxQrFgxTJ06FQDQuXNn3LlzB1KpFCdOnMCoUaO0KvOJEyeEx507d87O180XpFKp8NjMzAwuLi6QSCQICAjQ+Wd9/PgRI0eORHR0NExNTTF48GA0a9YMAHD16lXs2rULERERGDlyJDw8PFCyZEml67l+/Trmzp2LjIwMFC9eHCNHjkSNGjUQGxuLw4cP48KFC3j8+DHGjh2Lf/75h+d5IiIiogKIgRoiIiKiAs7e3h4uLi5yrzVs2BBdu3ZFp06dEBoaioCAAFy8eBFt2rQxUCn/m8LDwwEA5cqVM8jnX7x4EQkJCQCA2bNnY+bMmYiLi8OVK1f0ui8ULVoURYsWVfqeOA2csn33vyTrd69atSratGmDGjVqYOHChQCADRs2aBWoKVOmjML66tevjxYtWqBPnz6QSCTYs2cPfvnlF9jZ2eGnn37CvHnzkJiYmKNATdGiRYXRYAVJhQoVMHv2bFSrVg2VK1eGhYUF1q1bp5dAzZ9//ono6GgAwMqVK+V+x7p166Jq1aqYNGkSoqKisGbNGixdulRhHRKJBAsWLEBGRgaKFCmC/fv3w8nJSXi/cePGmDdvHvbt24f79+/j+PHjehmZR0RERET6ZWzoAhARERGRfhQpUkSu8VU2uoPyjixNkaHmjvD09ASQOQdQt27dhICR7HXKn/r164dvvvkGABAYGKiQNis7qlWrhnbt2gHI3B99fHwAZI6w+umnnwAAr1+/xpMnTzSu68GDB3j37h0AoG3btvl+7itlqlevjgEDBqBmzZqwsLDQ2+dEREQII6YaNWqkNNjWrl07NGrUCEBmSjZlv/PFixcREhICABgxYoRckEZm6tSpsLGxAQBs375dZ9+BiIiIiPIOAzVEREREXzFXV1fhcVhYmNplvb29MW3aNLRo0QI1atRA7dq10bFjRyxbtkwYGVJQTJ8+Ha6urmjevDmAzJEtS5YsQevWrVGjRg00aNAAw4cPx40bN3L8Ge/fv4erqytcXV3h4eEhvO7h4SG8LrN+/XrhNVdXV6F84hEJM2bMkFvG1dUV69aty3H5Pn36BC8vLwBAp06d5P6/deuW0NM/P8r6/b28vDB+/Hg0adIEVatWFX5XQPG3VkX8u7x//17lcikpKfj3338xaNAg/PDDD/juu+/QsGFDDB48GIcPH0ZaWppuvqQaxsbGqFChgvD848ePuVqfeP6TDx8+CI+7dOkiPD5+/LjG9YiXKYhpz/LSlStXkJGRAQDo1q2byuVko18yMjJw5coVhfcvX74sPHZ3d1e6jkKFCgkj5F69eoU3b97kuNxEREREZBgM1BARERF9xczMzITHqkZ1pKSkYPLkyRg0aBA8PT3x/v17JCcnIyEhAQEBAdixYwfatGmjtBGxIHjy5Anc3d2xa9cuBAcHIzk5GTExMbh+/TqGDRumNN3Q10A2z4mxsTE6duwIAOjYsSOMjIwgkUhw6tQpA5dQO3/++ScGDx6M8+fPIywsTK+BkhcvXqBt27ZYsGABvL29ERkZCYlEgujoaHh5eWH27Nno3bs3IiMj9VYGGfGxK36cE+JjPz09XXhcv359lCpVCgBw5swZtds2NTUV586dAwA4OTmhTp06uSrT1+7+/fvC43r16qlcTvzegwcPVK6nXLlycHBwULkeNzc3teshIiIiovyNc9QQERERfcWCgoKEx6VLl1Z4XyqVYvz48bh27RoAoFmzZmjbti3Kli0LY2NjPH78GDt37sSHDx8wfvx47N+/X5iwvCBISkrChAkT8OXLFwwfPhxNmjSBubk5/Pz8sHnzZkRERGDnzp0oVaoUBg0apJPPbNmyJb777jsAEAIkffr0Qd++fYVlbGxsMHToUHz69Ak///wzAGDixIkKc37Y29vnuByy0Q9ubm5wdHQEAJQtWxa1atXCgwcP4OnpiYEDB+Z4/XnhwoULCAgIgIuLCwYPHoyKFSsiJSUF/v7+Ov+st2/fon///vjy5QuKFCmCfv36oXr16ihZsiRiY2Nx5coVHDx4EE+ePMHo0aOxd+/eXAdQ1BEfu7I0aDklnn+lRIkSwmNZEG/Lli2IiorCrVu30LRpU6XruH79OmJjYwFwNI02Xr16BQCwtrZWG2ApUaIEihQpgvj4eLnfHAASEhKE0VTffvut2s8Tv591PURERESU/zFQQ0RERPSVSk9Pl5uvoHXr1grLHD58GNeuXYOZmRk2btyIxo0by71fs2ZNdO7cGf369UNgYCAWL16M/fv3673suhIdHQ0zMzPs3LlTrud69erV8dNPP6Fnz54ICwvDmjVr0LFjR9jZ2eX6M4sWLYqiRYvKvWZvb68w0bujoyOsrKzknmddJqf8/f3x8uVLAP+f7kymU6dOePDgAZ49e4ZXr17JpdjKbwICAtCwYUNs2bJFbj4UdSMUcmratGn48uULqlSpgu3btyvsC40aNULTpk0xYsQI+Pn54dixY+jZs6fOywFkBqiCg4MBAA0bNhTmH8mJ8PBwYa4UIyMjhW3XpUsXbNmyBQBw4sQJlYEaWeDPyMgoV4Ga6dOn49ixYzn+eyAz+PjPP//kah36JksXWbJkSY3LlipVCoGBgQrpKcXPNa1H/L6mNJdERERElP8w9RkRERHRV0aWpql///54/vw5gMwgTd26deWWk0ql2Lp1KwBgwIABCkEaGRsbG/z2228AMlPqyBqQC4pevXopbdh3dHTEtGnTAACJiYm5bjzOTzw9PQEAlpaWCgG6tm3bCiNBZMvlV8bGxli4cKHeJ62/d+8eHj58CABYunSpyoBd48aNhe0pnpdIF1JTUxEUFITNmzdj6tSpADLnHpk0aVK21yWVShETE4MzZ86gT58++Pz5M4DMyeuzjqwrX768MALs8uXLiI+PV1hfbGysMOqudu3aKFu2bLbL9F+TkJAAAHLBWFUKFSok9zdZ16HNesTvJyYmal1OIiIiIsofOKKGiIiIqIBbv3491q9fr/S9QoUKoXfv3pgyZYrCe69evcK7d+8AKB9tIyYOdDx69AjOzs45L3Aek03WrUyrVq1QtGhRfP78GXfu3BHSkBVkaWlpwvwzzZo1Q5EiReTet7W1RZMmTXDp0iWcPHkSkydPhrFx/uy/Vbt2bZQpU0bvnyObsL1cuXJwdXVVu2y9evVw9uxZPH36FGlpaSrnftKGus+qWrUqZs2ahRo1ami1Lk1p7KpVq4Z58+Ypfc/d3R1Pnz5FcnIyzp8/j27dusm9f/bsWUgkEgCZI3ByY9KkSRg6dGiu1iELbORnKSkpALSbX0gWiJT9jUxqaqrwWNN6xMHM5ORkrctJRERERPkDAzVEREREX7FKlSphwIABShv5nj59Kjzu1auX1uuMiIjQSdnygpmZGSpVqqT2/cqVK8PHx0duHo+C7NatW8Jk91nTnsl06tQJly5dQlhYGHx8fNCwYcO8LKLWNAVNdEV2LLx580brz5RIJIiLi8vVPEKqmJmZoVu3bqhTp06u1mNiYoJKlSqhS5cu6NOnj8rG/vbt22Pp0qWQSCQ4ceKEQqBGlvbMwsICbdq0yVWZHB0dhTmTvmYWFhZISkoSAlzqyAIyFhYWcq+Lgy+a1iMO6lhaWmanqERERESUDzBQQ0RERFTAiSeqT09PR1hYGM6fP4/jx4/j4cOHGDBgAI4cOaKQzikqKipHn6fP3tpSqTTbyxkZGalcztbWFiYmJmrXVbx4cQBAXFycVp+d38nSmdna2uLHH39UukyzZs2EkUSenp75NlCTda4ffYmOjs7R3yUlJeXqc2VzxwDA58+f8fLlS+zatQvv3r3D/PnzkZSUhF9++UWrdS1evBjVqlUDkHlMFCpUCMWLF9eq0b5YsWJo3LgxLl++DF9fX4SFhQlznrx7905ICyfbb0izwoULIykpSas0ZLL9qHDhwgrrkNG0HvH72qRbIyIiIqL8hYEaIiIiogIu60T1lStXRrNmzVC/fn1Mnz4doaGhmDVrFjZt2iT3dxkZGcLjv//+W2HuCnWfp2uWlpZITk7WOggkbiAvCGmQ8sqXL19w5coVAJnzisjmHlHnwoULmDt3br5s3NUUZNOV9PR0AJkj0FasWKH13+V2ZIj4uAWAunXronPnzujbty9evnyJP//8E25ubqhevbrGdZUpU0ZhfdnRpUsXXL58GRkZGThx4gSGDx8OADhx4oTcMrkVHh6e66BooUKF8v08OY6OjoiMjERYWJjGZT9+/AgAQnBMvA4ZTesRv591PURERESU/zFQQ0RERPSVcnd3x9WrV3H+/HlcuXIFXl5eciMnbG1thcfW1ta5auTNLRsbGyQnJwspuzQRL2djY6NyudjYWKSnp6tt8JetS916CoqzZ88qzHOhSWJiIi5cuKCTRnhDkI2oEgcelVE3+kV2LCQmJhr0OACAIkWKYPny5XB3d0daWhqWLVuGvXv36v1zmzZtCltbW8TGxuLkyZMKgRp7e3uVI7Sy488//8SxY8dytQ43Nzf8888/uS6LPlWoUAHPnj3Dly9fEBERAQcHB6XLffr0CfHx8QCA8uXLy71XpEgRlCpVCh8/fsTr16/Vfp74/azrISIiIqL8L3/OGkpEREREOjFp0iQhSPHnn3/KvVe5cmXh8YMHD/K0XFnJ5gX5+PGjVmmonj17pvC3ykgkErx48ULl+2lpacL7hmigV5e2LSdkac8cHBywevVqjf9kPe9lc5AURLL0UJ8/f1a73Js3b1S+V6VKFQBASEhIvpiDqVKlSujQoQMA4N69e7hx44beP9Pc3Bxt27YFAAQEBMDf3x8PHz7E27dvAWTOY2Nqyn5+2hLPL3T37l2Vy4nfq127tsr1vHnzRu2+6evrq3Y9RERERJS/MVBDRERE9BUrV66c0Pjq5+eH27dvC+9VrVpVaKg/dOhQtkdi6JJ4pI943g5lkpOTcfHiRQCZIyEqVaqkdnl1vfcvXrwopGEyxDwt4snDxZOB50RISIgQcGvdujXat2+v8d9PP/0EAPD29kZ4eHiuPt9QypQpAwBISEhQOeogNTUVFy5cULmO5s2bA8ic+2jPnj26L2QOjBw5EsbGmbdrWdMW6ot4VNXx48flAni6GnG1dOlSvHz5Mlf/8vtoGiBzn5L9fkePHlW5nIeHBwDA2NhY2A/FWrRoITxWdS5LSkrCuXPnAGSO5ClXrlyOy01EREREhsFADREREdFXbsSIEcLIDXGDr7GxMUaMGAEgs5F/6tSpaoMF8fHx+Pfff/VSxq5duwpzpGzYsAGBgYFKl5NKpVi4cKGQrqxPnz4wMzNTu+4DBw7g3r17Cq9HRERg+fLlADLnvHB3d8/NV8gRW1tbofzv3r3L1bqOHz8OqVQKIDNQow3ZchkZGUpH1QwYMACurq5wdXXF+/fvc1U+fXFzcxMe79y5U+kyS5cuVRuIatSokTAPzPbt23HmzBm1n/ny5UthLiB9KV++PFq1agUgc8Sbt7e3Xj8PAGrWrAlnZ2cAwKlTp3D27FkAQMWKFVG1alW9f35BounYcHBwQMeOHQEAt27dEgIpYmfPnsWtW7cAAJ07d1aaHq1Vq1bCfDybN29Wep5Yvny5EHD++eefc/6liIiIiMhgOHadiIiI6Cvn4uKC5s2b4/Lly7h79y7u3buHunXrAsgMdNy5cwcXL17EuXPn8Pz5c/Tq1QvVq1eHtbU14uPj8fr1a/j6+uLKlSswNzdH//79dV5GW1tbzJo1C7NmzUJcXBx69OiBnj174ocffoCDgwNSUlIQEBCAI0eO4PHjxwAyG49Hjhypdr12dnYoVKgQhg4disGDB6Nx48YwNzfHkydP8Pfff+PTp08AgAkTJsDe3l7n30sTU1NTVKtWDQ8ePMDRo0dRpUoVVK5cWUgxZWNjIzeXkDqyQIu9vb3w+2pSu3ZtODg4ICIiQm4C+YKkSpUqqFWrFh4+fIhDhw5BIpGgS5cusLa2xtu3b3Hw4EF4e3sLy6iyatUq9OjRA7GxsZg0aRJOnDiBdu3awdnZGcbGxoiKioK/vz+uXr2KR48eYejQoUpHQOjSyJEjcf78eQCZQdYGDRro9fOAzIDBX3/9JZdmq3Pnznr/3LwkG8Ui4+/vLzy+efMmQkNDhedOTk5aH09ZTZo0CTdv3kR0dDSmTJmCp0+fomnTpgCAa9euCYFFOzs7TJw4Uek6zMzM8Pvvv2PkyJGIj49Hnz59MGrUKFSvXh1xcXE4fPiwsI/UqVPnq/utiIiIiP4rGKghIiIi+g8YOXIkLl++DCCzwXf79u0AMudI+fPPP7Fo0SIcOHAA7969w4oVK1Sux87OTm9l7N69O9LT07Fo0SIkJSVh9+7d2L17t9Jl69Spg7Vr18LS0lLtOgsVKoS//voLw4YNw+bNm7F582aFZQYMGIAhQ4bo5DvkxIgRIzBy5EjExsZiypQpcu+NHTsW48aN07iO+/fvCz3tW7ZsKaRc0sTY2BitWrXCvn37EBgYiKdPn+K7774T3k9OTgaQ2VhcpEgRbb9Snlu0aBEGDBiAqKgoHDt2TCFF1NChQ1GxYkW1gRonJyccOHAA48ePR0BAAK5evYqrV6+qXF42N44+ValSBU2aNMH169fh7e2NR48eoWbNmnr9zM6dO2Pt2rXC6CxjY2N06tRJr5+Z12bMmKHyva1bt8o9d3d3z3GgplSpUvj7778xZswYREREYOvWrQrrd3BwwIYNG4Q0lMo0adIE8+bNw/z58xEZGYkFCxYoLFO9enWsX79emJOMiIiIiAoWpj4jIiIi+g+oXr06fvjhBwCZaXhko1KAzEb4P/74A8ePH8eAAQPg4uICa2trmJiYwNraGpUrV0b37t2xdu1aIRWSvvTq1QuXL1/GuHHjUKdOHdjZ2cHMzAxWVlZwcnJCx44dsWnTJuzduxfFixfXap3VqlXDsWPHMGDAADg5OcHCwgK2trb48ccfsWXLFsyePVuv30mTpk2bYteuXWjRogVKlCihMZWbMuK0ZdqmPZORzVMDAJ6ensLjlJQUYaRB586dtR7ZYwjly5fHsWPH0KdPH5QuXRpmZmaws7MTfuNp06ZptZ5y5crB09MTq1atQuvWrfHNN9/A0tISZmZmcHBwgJubG0aNGgUPDw+MHTtWz98qk3jU2MaNG/X+eaVLl0a9evWE5w0bNoSjo6PeP/drVaNGDZw4cQKjRo2Ci4sLrKysYGVlBRcXF4waNQonT55EjRo1NK6nZ8+e8PDwQM+ePVG2bFnhPFanTh388ccf2L9/v14D6URERESkX0ZSWVcpIiIiIqKvxPTp03Hs2DGULl1a73OJfK18fHwwcOBAmJqa4ty5c8I8GURERERERKRbHFFDREREREQK7t69CwDo2LEjgzRERERERER6xEANEREREREpuHv3LkxMTORSbxEREREREZHumRq6AERERERElP/s3r3b0EUgIiIiIiL6T+CIGiIiIiIiIiIiIiIiIgNhoIaIiIiIiIiIiIiIiMhAjKRSqdTQhSAiIiIiIiIiIiIiIvov4ogaIiIiIiIiIiIiIiIiA2GghoiIiIiIiIiIiIiIyEAYqCEiIiIiIiIiIiIiIjIQBmqIiIiIiIiIiIiIiIgMhIEaIiIiIiIiIiIiIiIiA2GghoiIiIiIiIiIiIiIyEAYqCEiIiIiIiIiIiIiIjIQBmqIiIiIiIiIiIiIiIgMhIEaIiIiIiIiIiIiIiIiAzE1dAGISF5MTIyhi/BVMDIygq2tLQAgNjYWUqnUsAUiAvdLyp+4X1J+ZBQZCVsXF7nXYgMCIC1e3EAlIsrEcyblR9wvKT/ifpn/FStWzNBFICIRjqghIiIiIiIiIiIiIiIyEAZqiIiIiIiIiIiIiIiIDISBGiIiIiIiIiIiIiIiIgNhoIaIiIiIiIiIiIiIiMhAGKghIiIiIiIiIiIiIiIyEAZqiIiIiIiIiIiIiIiIDISBGiIiIiIiIiIiIiIiIgNhoIaIiIiIiIiIiIiIiMhAGKghIiIiIiIiIiIiIiIyEAZqiIiIiIiIiIiIiIiIDISBGiIiIiIiIiIiIiIiIgNhoIaIiIiIiIiIiIiIiMhAGKghIiIiIiIiIiIiIiIyEAZqiIiIiIiIiIiIiIiIDISBGiIiIiIiIiIiIiIiIgNhoIaIiIiIiIiIiIiIiMhAGKghIiIiIiIiIiIiIiIyEAZqiIiIiIiIiIiIiIiIDISBGiIiIiIiIiIiIiIiIgNhoIaIiIiIiIiIiIiIiMhAGKghIiIiIiIiIiIiIiIyEAZqiIiIiIiIiIiIiIiIDISBGiIiIiIiIiIiIiIiIgNhoIaIiIiIiIiIiIiIiMhAGKghIiIiIiIiIiIiIiIyEAZqiIiIiIiIiIiIiIiIDMTU0AUgIiIiIiKinLt4WZqrv2/VwkhHJSEiIiIiopzgiBoiIiIiIiIiIiIiIiIDYaCGiIiIiIiIiIiIiIjIQBioISIiIiIiIiIiIiIiMhAGaoiIiIiIiIiIiIiIiAyEgRoiIiIiIiIiIiIiIiIDYaCGiIiIiIiIiIiIiIjIQBioISIiIiIiIiIiIiIiMhAGaoiIiIiIiIiIiIiIiAyEgRoiIiIiIiIiIiIiIiIDYaCGiIiIiIiIiIiIiIjIQBioISIiIiIiIiIiIiIiMhAGaoiIiIiIiIiIiIiIiAyEgRoiIiIiIiIiIiIiIiIDMTV0AYiIiIiIiMhwLl6W5vhvW7Uw0mFJiIiIiIj+mziihoiIiIiIiIiIiIiIyEAYqCEiIiIiIiIiIiIiIjIQBmqIiIiIiIiIiIiIiIgMhIEaIiIiIiIiIiIiIiIiA2GghoiIiIiIiIiIiIiIyEAYqCEiIiIiIiIiIiIiIjIQBmqIiIiIiIiIiIiIiIgMhIEaIiIiIiIiIiIiIiIiA2GghoiIiIiIiIiIiIiIyEAYqCEiIiIiIiIiIiIiIjIQBmqIiIiIiIiIiIiIiIgMhIEaIiIiIiIiIiIiIiIiA2GghoiIiIiIiIiIiIiIyEAYqCEiIiIiIiIiIiIiIjIQBmqIiIiIiIiIiIiIiIgMhIEaIiIiIiIiIiIiIiIiA2GghoiIiIiIiIiIiIiIyEBMDV0AIiIiIiKi/7KLl6WGLgIRERERERkQR9QQEREREREREREREREZCAM1REREREREREREREREBsJADRERERERERERERERkYEwUENERERERERERERERGQgpoYuABEREREREf03XbwszdXft2phpKOSEBEREREZDkfUEBERERERERERERERGQgDNURERERERERERERERAbCQA0REREREREREREREZGBMFBDRERERERERERERERkIAzUEBERERERERERERERGQgDNURERERERERERERERAbCQA0REREREREREREREZGBMFBDRERERERERERERERkIAzUEBERERERERERERERGQgDNURERERERERERERERAbCQA0REREREREREREREZGBMFBDRERERERERERERERkIAzUEBERERERERERERERGQgDNURERERERERERERERAbCQA0REREREREREREREZGBMFBDRERERERERERERERkIAzUEBERERERERERERERGQgDNURERERERERERERERAbCQA0REREREREREREREZGBMFBDRERERERERERERERkIAzUEBERERERERERERERGYipoQtAREREREREBdPFy1JDF4GIiIiIqMBjoIaIiIiIiCgXGKwgIiIiIqLcYOozIiIiIiIiIiIiIiIiA2GghoiIiIiIiIiIiIiIyEAYqCEiIiIiIiIiIiIiIjIQBmqIiIiIiIiIiIiIiIgMhIEaIiIiIiIiIiIiIiIiAzE1dAGIiIiIiIjo6/PxYyDu+h5DUNBdfPkcCRMTM9gWK4lKlX6EW/2usLa21+nnSSQSnDhxApcuXcLbt28RHx+PYsWKoXLlymjfvj1+/PFHrdbx6tUrPH/+HP7+/vD390dwcDDS09MBABs3bkSLFi10Wm4iIiIiIgZqiIiIiIiISKeuX9+NK5e2IiMjXXhNIklG2McvCPsYCF+fo+jWfS5cXBvq5PNCQ0MxdepUBAUFyb0eHh6O8PBwXLt2DU2bNsW8efNgYWGhcj2//PILXr58qZMyERERERFpi4EaIiIiIiIi0hlvr8O4dOFvAICJiSlq1GwD53K1kJGehsBAHzx/dhWJiXE4sH8Ghv68AWXKVs3V58XFxWHixIkICQkBADg7O6Njx44oUaIEQkJCcPz4cSFY88cff2DJkiUq15WRkSH33NHREWlpaYiKispVGYmIiIiI1GGghoiIiIiIiHQiLu4TLpzfAAAwNjbBgIGrUL6Cm/B+nbqd8ODBaRw7uhASSQqOH1+G0WN2w8jIKMefuXXrViFI06BBAyxbtkxu1Ey3bt0wbtw4BAQE4OrVq8LoGmXq1KmDJk2aoHLlyqhcuTLs7Owwf/58nDlzJsflIyIiIiLSxNjQBSAiIiIiIqKvw62beyGRpAAAvv+ht1yQRqZ27fao+l1zAEDYx0D4+9/I8edFRUXB09MTAFCoUCHMmTNHIbWZjY0N5s6dKwSDtm/frnJ9EydOxC+//IIffvgBdnZ2OS4XEREREVF2cEQNERERERHlSz6FCmFg2bIAgF/27sUvEyYgODgYBw8ehK+vLyIjI2FjY4PvvvsOgwcPhouLi/C3aWlpuHjxIk6cOIHg4GAkJiaiVKlS+Omnn9CvXz+185QAQEJCAjw9PeHl5YU3b97g8+fPsLKygpOTExo1aoTu3bujcOHCKv8+IyMDwW8eIDDQByEhTxEV+Q5JSZ9hYmKGIkXsUNapGurU6Yhy39ZWWw6PIwvw8GHmaI7Jv3qgWLFSCHh5B74+Hvjw4SUSE+NQuEgxlCtXGz82HgBHx2+13bw6J5VK8ezpFQCAkZERGjTooXLZhg17Css+fXIZVao0ydFn3rhxA2lpaQCAVq1aqQyulC9fHnXq1MG9e/cQGBiId+/ewcnJKUefSURERESkawzUEBERERFRgXDlyhXMnz8fycnJwmufPn3ClStXcOPGDSxbtgw//PADEhISMGPGDPj6+sr9fXBwMLZs2QIvLy+sW7cOlpaWSj/n5s2bWLRoEWJjY+Vej4uLw5MnT/DkyRMcOHAAS5YsQc2aNZWu49DB2Xj29KrC6+npaYiODkV0dCj8Hp1DjZpt0MV9BkxNzTV+f6k0A8c9l+Le3eNyr3+O+wS/R+fw9Mll9O6zCJUq/6hxXfoQHh6EL18iAQAOJcrBxtZR5bJlnarBwqIwUlISEPTKV+Vymvj4+AiPGzRooHbZhg0b4t69ewAAb29vBmqIiIiIKN9goIaIiIiIiPK9F69eYc/RozA3N0e/fv3g4uICiUSCa9eu4datW0hLS8Pvv/+OY8eOYd68efD19UXt2rXRrFkzFCtWDO/evcOhQ4cQGxuLJ0+eYPv27RgzZozC51y6dAlz5sxBRkYGzMzM0LRpU9SsWRPFihXD58+f4e3tjRs3biAmJgYTJkzAjh07ACiOYpFIUmBmZgHncrVRunRl2Nl9AzMzSyQkxCAyMgR+j84hKekz/B6dg6VFYXTo9KvGbXDp4mY8eXwR9sWdULNmW9jbl0FKSiKeP7+GwAAvpKdLcPTIAkyYdABFiuR92q5P4a+Fx6W/qaR2WWNjY5T6xgXBbx4iMTEOX75EwdraPtuf+fr1/39mpUrqP1P8/ps3b7L9WURERERE+sJADRERERER5Xu37t5F2bJlsWHDBpQoUUJ4vUOHDliyZAmOHz+OxMREjB8/Hi9fvsS4cePQr18/uXW0bNkSAwYMQEpKCo4dO4Zhw4bB3Pz/R7KEhYVh8eLFyMjIQOnSpbFq1So4OzvLraNLly7w8vLC1KlTkZKSgkWLFqFPP8U5Txr92A89e82HhYXy9GitfhoJj6ML8ezpFfj6euD7H3rDzr6M2m3w5PFF1KzVFl3cZ8LE5P9v5erW64TTp/6Et9chJCd/wYP7p9C4yUCFv4+NDcOHDy/Vfoa2/ve/Gihc2FbutcjIEOGxbbFSGtdha1tSeBwVFZLtQE1GRgZCQ0MBAP/H3n2HWVXd+wP+DAwdpCmKWMACYkHFXiMg1tijibElGjW5N/1Gozcx0TTTf+mxxqhJTCT2EhVBjYmICnaDKIiAgqB0hjqc3x9cjoPMDJ09g+/7PD7P5uy19/oOsxjPnM9eazVt2nS5cVGbrl3fr2nChAn1tAQAgA1LUAMAADQKl19+ea0fxp933nm5++67UyqV8uqrr+aggw5aIaRJkm222SZHHXVU7rrrrsyZMycvv/xy9txzz/L5P/3pT6mqqkrTpk3z4x//eIWQZpkDDjggZ599dq6//vq88sorefPN57Pttrsv16ZHj/r3nmnevFVOOvl/89roYVm4cF6ef/6h9Ot/br3XbLrZtjnhxEuXC2mWOXzgBRnxzF1ZtGhBXn/9qVqDmrFjR+SO275Xbx+r6tzzfrvC/jrz588uH7du3X6l96jZZv682fW0rN3ChVWprq5OkrRt2zaVlfX/etu+/fv9zZ69+v0BAMD60qToAgAAAFam9447Zpdddqn1XJcuXZabLXHKKafUeZ/dd38/UKm5/NWSJUvy0EMPJVm618n2229fbz1HHnlk+XjM60/XX3wdWrRok803X9rPxIkvr7T9vvuenMrKZnXea8tuvZMkU6cUs6zXooXv7x1UWdlipe1rtlm4cN5q91fzmpozo+rSosX7/c2bt/r9AQDA+mJGDQAA0OD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      "text/plain": [
       "<Figure size 600x700 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 711,
       "width": 821
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = run_scenario_value(\n",
    "    variants=[\"A\", \"B\"],\n",
    "    true_conversion_rates=[0.1, 0.1],\n",
    "    true_mean_purchase=[10, 10],\n",
    "    samples_per_variant=100000,\n",
    "    conversion_rate_prior=BetaPrior(alpha=5000, beta=5000),\n",
    "    mean_purchase_prior=GammaPrior(alpha=9000, beta=900),\n",
    "    comparison_method=\"best_of_rest\",\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a01ccc4a",
   "metadata": {},
   "source": [
    "* The 94% HDI contains 0 as expected."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9e7be20a",
   "metadata": {},
   "source": [
    "#### Scenario 2 - lower purchase rate, higher mean purchase, same overall revenue per visitor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "4b661564",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Sequential sampling (2 chains in 1 job)\n",
      "NUTS: [lam, theta]\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "    <div>\n",
       "        <style>\n",
       "            /* Turns off some styling */\n",
       "            progress {\n",
       "                /* gets rid of default border in Firefox and Opera. */\n",
       "                border: none;\n",
       "                /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
       "                background-size: auto;\n",
       "            }\n",
       "            .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
       "                background: #F44336;\n",
       "            }\n",
       "        </style>\n",
       "      <progress value='6000' class='' max='6000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
       "      100.00% [6000/6000 00:03<00:00 Sampling chain 0, 0 divergences]\n",
       "    </div>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "    <div>\n",
       "        <style>\n",
       "            /* Turns off some styling */\n",
       "            progress {\n",
       "                /* gets rid of default border in Firefox and Opera. */\n",
       "                border: none;\n",
       "                /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
       "                background-size: auto;\n",
       "            }\n",
       "            .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
       "                background: #F44336;\n",
       "            }\n",
       "        </style>\n",
       "      <progress value='6000' class='' max='6000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
       "      100.00% [6000/6000 00:03<00:00 Sampling chain 1, 0 divergences]\n",
       "    </div>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 2 chains for 1_000 tune and 5_000 draw iterations (2_000 + 10_000 draws total) took 6 seconds.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x700 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 711,
       "width": 821
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "scenario_value_2 = run_scenario_value(\n",
    "    variants=[\"A\", \"B\"],\n",
    "    true_conversion_rates=[0.1, 0.08],\n",
    "    true_mean_purchase=[10, 12.5],\n",
    "    samples_per_variant=100000,\n",
    "    conversion_rate_prior=BetaPrior(alpha=5000, beta=5000),\n",
    "    mean_purchase_prior=GammaPrior(alpha=9000, beta=900),\n",
    "    comparison_method=\"best_of_rest\",\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7fd5b4aa",
   "metadata": {},
   "source": [
    "* The 94% HDI for the average revenue per visitor (RPV) contains 0 as expected.\n",
    "* In these cases, it's also useful to plot the relative uplift distributions for `theta` (the purchase-anything rate) and `1 / lam` (the mean purchase value) to understand how the A/B test has affected visitor behaviour. We show this below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "68a7a343",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1656x552 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 563,
       "width": 1667
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "axs = az.plot_posterior(\n",
    "    scenario_value_2,\n",
    "    var_names=[\"theta_reluplift_1\", \"reciprocal_lam_reluplift_1\"],\n",
    "    textsize=10,\n",
    "    kind=\"hist\",\n",
    ")\n",
    "axs[0].set_title(f\"Conversion Rate Uplift B, True Uplift = {(0.04 / 0.05 - 1):.2%}\", fontsize=10)\n",
    "axs[0].axvline(x=0, color=\"red\")\n",
    "axs[1].set_title(\n",
    "    f\"Revenue per Converting Visitor Uplift B, True Uplift = {(25 / 20 - 1):.2%}\", fontsize=10\n",
    ")\n",
    "axs[1].axvline(x=0, color=\"red\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8786b390",
   "metadata": {},
   "source": [
    "* Variant B's conversion rate uplift has a HDI well below 0, while the revenue per converting visitor has a HDI well above 0. So the model is able to capture the reduction in purchasing visitors as well as the increase in mean purchase amount."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1873dc0a",
   "metadata": {},
   "source": [
    "#### Scenario 3 - Higher propensity to purchase and mean purchase value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "db019cc9",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Sequential sampling (2 chains in 1 job)\n",
      "NUTS: [lam, theta]\n"
     ]
    },
    {
     "data": {
      "text/html": [
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       "            progress {\n",
       "                /* gets rid of default border in Firefox and Opera. */\n",
       "                border: none;\n",
       "                /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
       "                background-size: auto;\n",
       "            }\n",
       "            .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
       "                background: #F44336;\n",
       "            }\n",
       "        </style>\n",
       "      <progress value='6000' class='' max='6000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
       "      100.00% [6000/6000 00:02<00:00 Sampling chain 0, 0 divergences]\n",
       "    </div>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
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       "    <div>\n",
       "        <style>\n",
       "            /* Turns off some styling */\n",
       "            progress {\n",
       "                /* gets rid of default border in Firefox and Opera. */\n",
       "                border: none;\n",
       "                /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
       "                background-size: auto;\n",
       "            }\n",
       "            .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
       "                background: #F44336;\n",
       "            }\n",
       "        </style>\n",
       "      <progress value='6000' class='' max='6000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
       "      100.00% [6000/6000 00:02<00:00 Sampling chain 1, 0 divergences]\n",
       "    </div>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 2 chains for 1_000 tune and 5_000 draw iterations (2_000 + 10_000 draws total) took 6 seconds.\n"
     ]
    },
    {
     "data": {
      "image/png": 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AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 600x700 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 711,
       "width": 821
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = run_scenario_value(\n",
    "    variants=[\"A\", \"B\"],\n",
    "    true_conversion_rates=[0.1, 0.11],\n",
    "    true_mean_purchase=[10, 10.5],\n",
    "    samples_per_variant=100000,\n",
    "    conversion_rate_prior=BetaPrior(alpha=5000, beta=5000),\n",
    "    mean_purchase_prior=GammaPrior(alpha=9000, beta=900),\n",
    "    comparison_method=\"best_of_rest\",\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dec9cb93",
   "metadata": {},
   "source": [
    "* The 94% HDI is above 0 for variant B as expected.\n",
    "\n",
    "Note that one concern with using value conversions in practice (that doesn't show up when we're just simulating synthetic data) is the existence of outliers. For example, a visitor in one variant could spend thousands of dollars, and the observed revenue data no longer follows a 'nice' distribution like Gamma. It's common to impute these outliers prior to running a statistical analysis (we have to be careful with removing them altogether, as this could bias the inference), or fall back to bernoulli conversions for decision making."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6dff0b91",
   "metadata": {},
   "source": [
    "### Further Reading\n",
    "\n",
    "There are many other considerations to implementing a Bayesian framework to analyse A/B tests in practice. Some include:\n",
    "\n",
    "* How do we choose our prior distributions? \n",
    "* In practice, people look at A/B test results every day, not only once at the end of the test. How do we balance finding true differences faster vs. minizing false discoveries (the 'early stopping' problem)?\n",
    "* How do we plan the length and size of A/B tests using power analysis, if we're using Bayesian models to analyse the results?\n",
    "* Outside of the conversion rates (bernoulli random variables for each visitor), many value distributions in online software cannot be fit with nice densities like Normal, Gamma, etc. How do we model these?\n",
    "\n",
    "Various textbooks and online resources dive into these areas in more detail. [Doing Bayesian Data Analysis](http://doingbayesiandataanalysis.blogspot.com/) by John Kruschke is a great resource, and has been translated to PyMC3 here: https://github.com/JWarmenhoven/DBDA-python.\n",
    "\n",
    "We also plan to create more PyMC3 tutorials on these topics, so stay tuned!\n",
    "\n",
    "---\n",
    "\n",
    "Author: [Cuong Duong](https://github.com/tcuongd) (2021-05-23)\n",
    "\n",
    "### References\n",
    "\n",
    "* [Stucchio, C. (2015) _Bayesian A/B Testing at VWO_](https://vwo.com/downloads/VWO_SmartStats_technical_whitepaper.pdf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "a1a4b30a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Last updated: Thu May 27 2021\n",
      "\n",
      "Python implementation: CPython\n",
      "Python version       : 3.8.6\n",
      "IPython version      : 7.23.1\n",
      "\n",
      "theano: 1.1.2\n",
      "xarray: 0.18.0\n",
      "\n",
      "pymc3     : 3.11.2\n",
      "arviz     : 0.11.2\n",
      "matplotlib: 3.4.2\n",
      "pandas    : 1.2.4\n",
      "numpy     : 1.20.3\n",
      "\n",
      "Watermark: 2.2.0\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -n -u -v -iv -w -p theano,xarray"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
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