Bootstrap.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "4d524a13-9dac-4432-9d6c-880723143f21",
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.stats as stats\n",
    "import numpy\n",
    "import matplotlib.pyplot as pyplot\n",
    "from collections import Counter, defaultdict\n",
    "\n",
    "from scipy.stats import (\n",
    "    norm, binom, expon, t, chi2, pareto, ttest_ind, sem, beta, laplace, ttest_1samp\n",
    ")\n",
    "from statsmodels.stats.proportion import proportion_confint\n",
    "import numpy as numpy\n",
    "from seaborn import distplot\n",
    "from matplotlib import pyplot\n",
    "import seaborn\n",
    "from tqdm.notebook import tqdm\n",
    "\n",
    "import sys\n",
    "sys.path.append('.')\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "e03d6f05-f72e-43ba-abf4-803cc4eddd67",
   "metadata": {},
   "outputs": [],
   "source": [
    "def inverse_plot_colorscheme():\n",
    "    import cycler\n",
    "    def invert(color_to_convert): \n",
    "        table = str.maketrans('0123456789abcdef', 'fedcba9876543210')\n",
    "        return '#' + color_to_convert[1:].lower().translate(table).upper()\n",
    "    update_dict = {}\n",
    "    for key, value in pyplot.rcParams.items():\n",
    "        if value == 'black':\n",
    "            update_dict[key] = 'white'\n",
    "        elif value == 'white':\n",
    "            update_dict[key] = 'black'\n",
    "    \n",
    "    old_cycle = pyplot.rcParams['axes.prop_cycle']\n",
    "    new_cycle = []\n",
    "    for value in old_cycle:\n",
    "        new_cycle.append({\n",
    "            'color': invert(value['color'])\n",
    "        })\n",
    "    pyplot.rcParams.update(update_dict)\n",
    "    pyplot.rcParams['axes.prop_cycle'] = cycler.Cycler(new_cycle)\n",
    "    lec = pyplot.rcParams['legend.edgecolor']\n",
    "    lec = str(1 - float(lec))\n",
    "    pyplot.rcParams['legend.edgecolor'] = lec"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "ab433bcb-709f-4f9c-bc95-d52b7e834a33",
   "metadata": {},
   "outputs": [],
   "source": [
    "inverse_plot_colorscheme()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "c1bb4260-f23c-4888-9e73-c2ddd4d96698",
   "metadata": {},
   "outputs": [],
   "source": [
    "# s1 = stats.gamma(a=1.75, scale=2).rvs(1000)\n",
    "# s2 = stats.gamma(a=1.75, scale=2).rvs(1000)\n",
    "\n",
    "\n",
    "# numpy.quantile(s1, 0.75)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "28a2322b-cc1e-4dc7-a969-d16f4acba570",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "a4301903-269c-4b38-b9ab-f70311e80d0b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# numpy.save('bootstrap_example_1.npy', s1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cc0d5f9f-9db4-4e79-ac94-003d57924ad5",
   "metadata": {},
   "source": [
    "# Лекция X. Bootstrap\n",
    "\n",
    "На этой лекции мы рассмотрим один из главных методов статистики, который позволит вам построить критерий для любой сколь угодно сложной гипотезы, которая может у вас возникнуть на практике.\n",
    "\n",
    "Давайте рассмотрим следующую задачу:\n",
    "\n",
    "> 📈 **Задача**\n",
    ">\n",
    "> Вы работаете аналитиком в такси. Недавно один из менеджеров компании пришел к нам с идеей, что у нас в приложении часто выбирается водитель, который очень далеко от пользователя. И это приводит к оттоку пользователей нашего сервиса.\n",
    ">\n",
    "> Для того, чтобы в будущем оценить, насколько вы улучшили алгоритм подбора водителей, вы решаете использовать 75 процентиль распределения времени ожидания такси как основную метрику качества алгоритма. Ваша задача сейчас оценить текущее значение метрики, чтобы в будущем использовать это значение как бейзлайн.\n",
    "\n",
    "Запишем задачу на языке математики:\n",
    "\n",
    "- Пусть $X$ &mdash; выборка метрики времени ожидания такси пользователем, $X_{[0.75]}$ &mdash; 75 процентиль этой выборки.\n",
    "\n",
    "А теперь посмотрим на данные:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d9ffbbc8-45ed-4d11-979f-5e705ebade56",
   "metadata": {},
   "outputs": [],
   "source": [
    "sample = numpy.load('bootstrap_example_1.npy')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "9dd15102-2b3a-45e9-b362-c107fd4df777",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "dark"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.figure(figsize=(10, 5))\n",
    "pyplot.title('Время ожидания такси пользователями', fontsize=12)\n",
    "seaborn.histplot(sample, stat='density')\n",
    "pyplot.xlabel('Время(минуты)', fontsize=12)\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "fac010ef-faf6-49e2-96e0-c69dc40d3357",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Оценка 75 процентили: 4.596\n"
     ]
    }
   ],
   "source": [
    "print(f\"Оценка 75 процентили: {round(numpy.percentile(sample, 75), 3)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "72d00f47-7478-4df4-8a38-96e460f5504f",
   "metadata": {},
   "source": [
    "Мы получили некоторую оценку. Нужно построить для нее доверительный интервал.\n",
    "\n",
    "Но пока мы не знаем как это сделать.\n",
    "\n",
    "----\n",
    "\n",
    "### Идея 1: Монте-Карло\n",
    "\n",
    "Для того, чтобы решить задачу, перейдем к более простой выборке, у которой мы уже все знаем: и распределение, из которого она сгенерирована, и истинный квантиль. И на ее примере попытаемся решить задачу."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "1ac7e2c3-6bde-46ed-94e1-4671bf78160f",
   "metadata": {},
   "outputs": [],
   "source": [
    "numpy.random.seed(42)\n",
    "N = 20000\n",
    "example_dist = stats.gamma(a=2, scale=3)\n",
    "example_sample = example_dist.rvs(N)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "37885839-da93-456a-899b-d62316225678",
   "metadata": {},
   "source": [
    "- Пусть $\\theta$ &mdash; истинное значение квантили, которое мы не знаем. В общем случае это может быть любая характеристика: мат. ожидание, дисперсия и т.д.\n",
    "- $\\widehat{\\theta}$ &mdash; полученная оценка $\\theta$ по выборке. В изначальной задаче ее реализация равна 4.596.\n",
    "\n",
    "Давайте посмотрим, чему они равны в нашем искусственном примере."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "da5ca797-b1ab-411b-a616-33a50ef5ae79",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "theta = 8.078\n",
      "theta estim = 8.106\n"
     ]
    }
   ],
   "source": [
    "theta = example_dist.ppf(0.75)\n",
    "theta_estim = numpy.percentile(example_sample, 75)\n",
    "\n",
    "print(f\"theta = {round(theta, 3)}\")\n",
    "print(f\"theta estim = {round(theta_estim, 3)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "61f521cd-8cfc-48b9-ba44-c978d54e7d02",
   "metadata": {},
   "source": [
    "Как посторить доверительный интервал для $\\theta$? \n",
    "\n",
    "1. Для этого предлагаю первым шагом построить распределение $\\Delta = \\widehat{\\theta} - \\theta$.\n",
    "    - Смысл &mdash; понять, насколько может шуметь оценка относительно истинного значения. Далее, с помощью этого распределения мы и построим дов. интервал.\n",
    "    - Пока мы будем исходить, что мы знаем $\\theta$ и истинное распределение. Но далее мы сможем избавиться от этого.\n",
    "\n",
    "Построим это распределение для нашей искусственной задачи. Давайте воспользуемся любимым методом: Монте-Карло. \n",
    "\n",
    "Мы построим выборку $\\Delta_1,\\ \\dots,\\ \\Delta_B $. Для этого:\n",
    "\n",
    "- Насемплируем `B` раз из нашего распределения `example_dist` выборку.\n",
    "    - `B` возьмем достаточно большим: например, 10000.\n",
    "    - Размер каждой выборки равен N, изначальному размеру выборки. Ведь мы хотим оценить $\\widehat{\\theta} - \\theta$, где $\\widehat{\\theta}$построена по выборке размера N. Если взять слишком большую выборку (размера бесконечность), то у вас не будет шума и $\\Delta = 0$, хотя для выборки размера $N$ шум будет.\n",
    "- Посчитаем в каждом случае $\\widehat{\\theta_i}$.\n",
    "- А дальше вычтем из этого значения $\\theta$. Получим `B` значений $\\Delta_i = \\widehat{\\theta_i} - \\theta$.\n",
    "\n",
    "Напишем функцию генерации выборки $\\widehat{\\theta_i}$. Эта функция будет основой нашего будущего алгоритма."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "1f945bd6-d519-4f19-a03b-b069b229ad36",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_estim_theta_sample(sample_len, gen_sample_func, theta_func, B=10000):\n",
    "    \"\"\"\n",
    "        Функция для генерации выборки theta estim.\n",
    "    \n",
    "        Праметры:\n",
    "            - sample_len: какого размера выборку надо генерировать. \n",
    "                - sample_len = len(sample)\n",
    "            - gen_sample_func: генерация выборки из нашего распределения, принимающая на вход лишь размер выборки. \n",
    "                - Например, gen_sample_func = lambda N: stats.norm().rvs(N)\n",
    "            - theta_func: функция генерации оценки theta по выборке.\n",
    "                - Например, lambda sample: numpy.percentile(sample, 75)\n",
    "            - B: сколько выборок надо сгенерировать, какого размера будет массив theta estim\n",
    "        Возвращает:\n",
    "            - Массив theta_estim_array размера B \n",
    "    \"\"\"\n",
    "    \n",
    "    theta_estim_array = []\n",
    "    for _ in range(B):\n",
    "        curr_sample = gen_sample_func(sample_len)\n",
    "        theta_estim = theta_func(curr_sample)\n",
    "        theta_estim_array.append(theta_estim)\n",
    "    return theta_estim_array"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c963209b-10fe-45e5-bc97-fda4add8651c",
   "metadata": {},
   "source": [
    "Теперь с помощью этого массива получим текущий массив $\\Delta$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "86e70f1e-7840-4972-91c0-33d393d087a9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "dark"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gen_sample_func = lambda N: example_dist.rvs(N)\n",
    "theta_func = lambda sample: numpy.percentile(sample, 75)\n",
    "\n",
    "theta_estim_array = get_estim_theta_sample(len(example_sample), gen_sample_func, theta_func, B=10000)\n",
    "delta = theta_estim_array - theta\n",
    "\n",
    "pyplot.figure(figsize=(10, 5))\n",
    "pyplot.title('Гистограмма $\\Delta$', fontsize=12)\n",
    "seaborn.histplot(delta, stat='density', alpha=0.5)\n",
    "pyplot.xlabel('$\\Delta$', fontsize=12)\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c305e8f-0beb-4247-9670-d8907d7e118d",
   "metadata": {},
   "source": [
    "2. Следующим шагом рассмотрим $\\alpha/2, 1 - \\alpha/2$ квантили этого распределения: $\\Delta_{[\\alpha/2]}, \\Delta_{[1 - \\alpha/2]}$. Тогда по определению квантилей $P(\\Delta_{[\\alpha/2]} < \\widehat{\\theta} - \\theta < \\Delta_{[1 - \\alpha/2]}) = 1 - \\alpha$.\n",
    "    - В случае, когда у нас есть выборка размера B, мы можем взять оценки квантилей. Поэтому чем больше B, тем точнее получится оценка.\n",
    "3. $P(\\widehat{\\theta} - \\Delta_{[1 - \\alpha/2]} < \\theta < \\widehat{\\theta} - \\Delta_{[\\alpha/2]}) = 1 - \\alpha$. \n",
    "    - Таким образом, по определению доверительного интервала, $CI = (\\widehat{\\theta} - \\Delta_{[1 - \\alpha/2]}, \\widehat{\\theta} - \\Delta_{[\\alpha/2]})$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "99436291-a6cd-433e-8943-08c04416f940",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Истинное theta: 8.08\n",
      "Полученный CI: (8.01, 8.2)\n"
     ]
    }
   ],
   "source": [
    "alpha = 0.05\n",
    "left_delta, right_delta = numpy.quantile(delta, [alpha/2, 1-alpha/2])\n",
    "\n",
    "left_bound, right_bound = theta_estim - right_delta, theta_estim - left_delta\n",
    "print(f\"Истинное theta: {round(theta, 2)}\")\n",
    "print(f\"Полученный CI: ({round(left_bound, 2)}, {round(right_bound, 2)})\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8fee8b89-f80a-44ff-ab67-8929af831b3a",
   "metadata": {},
   "source": [
    "Мы видим, что истинное theta попало в дов. интервал.\n",
    "\n",
    "Мы построили дов. интервал с учетом знания $\\theta$ и истинного распределения выборки, но в реальности мы их не знаем. И тут приходит на помощь еще 1 хак.\n",
    "\n",
    "---\n",
    "\n",
    "### Идея 2: Эмпирическое распределение вместо истинного\n",
    "\n",
    "Чтобы построить дов. интервал, мы должны как-то получить $\\Delta_{[\\alpha/2]}, \\Delta_{[1 - \\alpha/2]}$.\n",
    "\n",
    "Вспомним, как определяется $\\Delta:\\ \\Delta = \\widehat{\\theta} - \\theta$. Для того, чтобы ее посчитать, мы использовали истинное значение $\\theta$ и истинное распределение для генерации $\\widehat{\\theta}$.\n",
    "\n",
    "**Но что если вместо истинного $\\theta$ и истинного распределения использовать их приближения?**\n",
    "\n",
    "Что здесь предлагается:\n",
    "\n",
    "- У нас есть истинное распределение `dist` и истинная характеристика $\\theta$ этого распределения. \n",
    "- Но мы их не знаем. Так давайте заменим истинное распределение на эмпирическое распределение. И тэту возьмем как характеристику этого эмпирического распределения.\n",
    "\n",
    "#### Вспомним, что такое эмпирическое распределение, и чем оно хорошо.\n",
    "\n",
    "С эмпирическим распределением мы встречались, когда строили критерии согласия и однородности Колмогорова-Смирнова. Как оно строится?\n",
    "\n",
    "0. Пусть $X_1, ..., X_n$ выборка из изначального распределения.\n",
    "1. Функция распределения эмпирического распределения равна \n",
    "\n",
    "$$\\widehat{F_n}(x) = \\frac{1}{n}\\sum_i[X_i \\leqslant x]$$\n",
    "\n",
    "2. Теперь несложно показать, что чтобы построить выборку из эмпирического распределения, мы должны насемплировать **с возвращением** из изначальной выборки новую выборку нужного нам размера.\n",
    "    - С возвращением означет, что каждый новый элемент равновероятно выбирается из всех элементов выборки, а не только из тех, что не были использованы ранее. При этом, если какой-то элемет встречается в N раз чаще другого, то в насемплированной выборке он также будет в среднем встречаться в N раз чаще.\n",
    "\n",
    "Рассмотрим на примере.\n",
    "\n",
    "- `numpy.random.choice` &mdash; [функция](https://numpy.org/doc/stable/reference/random/generated/numpy.random.choice.html), решающая на Python эту задачу."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "4d179606-c87e-4d68-a146-b3ad863408cd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 2, 3, 2, 2, 4, 2, 2, 4, 4])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = [2, 3, 4, 2]\n",
    "\n",
    "# Насемплируем выборку размера 10 из эмпирического распределения, полученного по выборке X\n",
    "emp_dist_X_gen = numpy.random.choice(X, replace=True, size=10)\n",
    "emp_dist_X_gen"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "708bfb7d-f76a-493a-8611-9dbc44d23e3d",
   "metadata": {},
   "source": [
    "\n",
    "Чем хорошо эмпирическое распределение?\n",
    "- Тем, что у него все характеристики известны.\n",
    "- И оно сходится к истинному распределению на бесконечности (о чем мы уже говорили ранее).\n",
    "\n",
    "\n",
    "Но какая будет характеристика $\\theta$ у эмпирического распределения? Она не равна изначальной $\\theta$! А будет равна оценке $\\widehat{\\theta}$ у изначальной выборки. \n",
    "\n",
    "А значит теперь мы можем посчитать $\\Delta^*$, полученное из эмпирического распределения. Ведь для этого нам нужны были:\n",
    "- `sample_size` (не изменилось)\n",
    "- `gen_sample_func`. Вместо истинного распределения теперь мы подставляем функцию получения выборки с возвращением.\n",
    "- `theta_func` (не изменилось)\n",
    "- `B` (не изменилось)\n",
    "- `theta` поменялось на `theta_estim`\n",
    "\n",
    "Сравним код, который был, с новым кодом."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "81d86ee7-8190-4b60-9971-cf72b5fe2ae1",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Было - стало\n",
    "# gen_sample_func = lambda N: example_dist.rvs(N)\n",
    "gen_sample_func = lambda N: numpy.random.choice(example_sample, replace=True, size=N)\n",
    "\n",
    "# theta_func = lambda sample: numpy.percentile(sample, 75)\n",
    "theta_func = lambda sample: numpy.percentile(sample, 75) # не изменилось\n",
    "\n",
    "# theta_estim_array = get_estim_theta_sample(len(example_sample), gen_sample_func, theta_func, B=10000)\n",
    "theta_estim_asterisk_array = get_estim_theta_sample(len(example_sample), gen_sample_func, theta_func, B=10000)\n",
    "\n",
    "# delta = theta_estim_array - theta\n",
    "delta_asterisk = theta_estim_asterisk_array - theta_estim"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1dea42b5-05db-41e2-97a5-a826ce11d322",
   "metadata": {},
   "source": [
    "### Главное допущение bootstrap: $\\Delta \\approx \\Delta^*$.\n",
    "- А на бесконечности это верно, потому что эмпирическое распределение равно истинному распределению.\n",
    "\n",
    "Давайте проверим это допущение на примере:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "ebe24bad-08b5-4b16-abff-f10aa5769cc1",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "dark"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.figure(figsize=(10, 5))\n",
    "pyplot.title('Гистограмма сравнения $\\Delta$ с $\\Delta^*$', fontsize=12)\n",
    "seaborn.histplot(delta, stat='density', alpha=0.5, label='$\\Delta$')\n",
    "seaborn.histplot(delta_asterisk, stat='density', alpha=0.5, color='lime', label='$\\Delta^*$')\n",
    "pyplot.legend(fontsize=12)\n",
    "pyplot.xlabel('$\\Delta$', fontsize=12)\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1330de2a-5f83-4733-95c7-9e1ee70fb229",
   "metadata": {},
   "source": [
    "Мы видим, что распределения похожи, хоть и не идентичны.\n",
    "\n",
    "Но исходя из нашего допущения мы можем заменить \n",
    "- $CI = (\\widehat{\\theta} - \\Delta_{[1 - \\alpha/2]}, \\widehat{\\theta} - \\Delta_{[\\alpha/2]})$ на\n",
    "- $CI = (\\widehat{\\theta} - \\Delta^*_{[1 - \\alpha/2]}, \\widehat{\\theta} - \\Delta^*_{[\\alpha/2]})$\n",
    "    - Что такое $\\Delta^*_i$? Это $ \\theta^*_i - \\widehat{\\theta}$, где $\\theta^*_i$ &mdash; оценка $\\widehat{\\theta}$, полученная по i-ой выборке, сгенерированной из эмпирического распределения!\n",
    "    - Перепишем: $CI = (\\widehat{\\theta} - \\theta^*_{[1 - \\alpha/2]} + \\widehat{\\theta}, \\widehat{\\theta} - \\theta^*_{[\\alpha/2]} + \\widehat{\\theta})$\n",
    "\n",
    "\n",
    "Итого: $CI = (2\\widehat{\\theta} - \\theta^*_{[1 - \\alpha/2]}, 2\\widehat{\\theta} - \\theta^*_{[\\alpha/2]})$. Так и строится полноценный бутстрап критерий!\n",
    "\n",
    "\n",
    "**Главная проблема перехода к эмпирическому распределению:** ваше распределение не равно изначальному! Поэтому все характеристики этого распределения не равны характеристикам исходного распределения. И очень часто, забывая про это, вы можете начать использовать бутстрап неверно!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "dfbda5b8-5a2a-4cd5-bfee-ba1721134d39",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Истинное theta: 8.08\n",
      "Полученный CI: (8.02, 8.19)\n"
     ]
    }
   ],
   "source": [
    "alpha = 0.05\n",
    "left_theta_asterisk, right_theta_asterisk = numpy.quantile(theta_estim_asterisk_array, [alpha/2, 1-alpha/2])\n",
    "\n",
    "left_bound, right_bound = 2 * theta_estim - right_theta_asterisk, 2 * theta_estim - left_theta_asterisk\n",
    "print(f\"Истинное theta: {round(theta, 2)}\")\n",
    "print(f\"Полученный CI: ({round(left_bound, 2)}, {round(right_bound, 2)})\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c4e3481-1834-4985-84f6-a406085fac5a",
   "metadata": {},
   "source": [
    "Давайте напишем теперь полноценный код бутстрап-критерия. Что мы сделали по шагам:\n",
    "\n",
    "1. Считаем $\\widehat{\\theta}$ по изначальной выборке.\n",
    "2. Написали генерацию выборок из эмпирического распределения: `lambda N: numpy.random.choice(example_sample, replace=True, size=N)`. \n",
    "3. Написали функцию генерации $\\theta^*$ (использовав логику Монте-Карло).\n",
    "    - Выборки, которые будут сгенерированны внутри этого шага в цикле с помощью шага 1, называются **бутстрап**-выборками.\n",
    "4. Считаем левый и правый квантили $\\theta^*_{[\\alpha/2]}, \\theta^*_{[1 - \\alpha/2]}$.\n",
    "5. Считаем $CI = (2\\widehat{\\theta} - \\theta^*_{[1 - \\alpha/2]}, 2\\widehat{\\theta} - \\theta^*_{[\\alpha/2]})$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "c99ca62a-0141-43b2-9d89-dc47d6e48db6",
   "metadata": {},
   "outputs": [],
   "source": [
    "def raw_bootstrap(sample, theta_func, alpha = 0.05):\n",
    "    B = 10000\n",
    "    \n",
    "    theta_estim = theta_func(sample)\n",
    "    gen_sample_func = lambda N: numpy.random.choice(sample, replace=True, size=N)\n",
    "    \n",
    "    theta_estim_asterisk_array = get_estim_theta_sample(len(example_sample), gen_sample_func, theta_func, B)\n",
    "    left_theta_asterisk, right_theta_asterisk = numpy.quantile(theta_estim_asterisk_array, [alpha/2, 1-alpha/2])\n",
    "    left_bound, right_bound = 2 * theta_estim - right_theta_asterisk, 2 * theta_estim - left_theta_asterisk\n",
    "\n",
    "    return left_bound, right_bound"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "778343a1-c98d-4c55-9d43-ca3316211d81",
   "metadata": {},
   "source": [
    "Проверим работоспособность:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "24fccb96-991d-45e5-99df-89bc7024f66c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(8.020543156899208, 8.194299412190123)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "numpy.random.seed(42)\n",
    "N = 20000\n",
    "example_dist = stats.gamma(a=2, scale=3)\n",
    "example_sample = example_dist.rvs(N)\n",
    "\n",
    "theta_func = lambda sample: numpy.percentile(sample, 75)\n",
    "raw_bootstrap(example_sample, theta_func, alpha = 0.05)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10b9ccc2-e0ee-4905-b649-709f6176cb85",
   "metadata": {},
   "source": [
    "Да, все отлично!\n",
    "\n",
    "## Более простой алгоритм бутстрапа\n",
    "\n",
    "Давайте чуть упростим шаги:\n",
    "\n",
    "1. Считаем $\\widehat{\\theta}$ по изначальной выборке.\n",
    "2. В цикле размера `B`:\n",
    "    1. Генерируем выборку с возвращением из изначальной выборки. Размер `N` &mdash; изначальный размер выборки.  Эта выборка называется **бутстрап-выборкой**.\n",
    "    2. Считаем по этой выборке $\\theta^*_i$ точно так же, как считаем $\\widehat{\\theta}$ по изначальной выборке.\n",
    "3. Сохраняем $\\theta^*_1,\\ ...,\\ \\theta^*_B$ в массив.\n",
    "4. Строим доверительный интервал:\n",
    "    1. Считаем левый и правый квантили $\\theta^*_{[\\alpha/2]}, \\theta^*_{[1 - \\alpha/2]}$.\n",
    "    2. $CI = (2\\widehat{\\theta} - \\theta^*_{[1 - \\alpha/2]}, 2\\widehat{\\theta} - \\theta^*_{[\\alpha/2]})$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "f49a8539-6ced-4e59-8948-bc96c931b2a0",
   "metadata": {},
   "outputs": [],
   "source": [
    "def bootstrap_ci(sample, theta_func, alpha=0.05):\n",
    "    \"\"\"\n",
    "        Функция для построения доверительного интервала через бутстрап\n",
    "        \n",
    "        Параметры:\n",
    "            - sample: изначальная выборка\n",
    "            - theta_func: функция генерации оценки theta по выборке.\n",
    "                - Например, lambda sample: numpy.percentile(sample, 75)\n",
    "            - alpha: уровень значимости критерия. Доверительный интервал будет ширины 1-alpha.\n",
    "        Возвращает:\n",
    "            - левую и правую границы дов. интервала.\n",
    "    \"\"\"\n",
    "    \n",
    "    B = 2000 # Чтобы ускорить работу\n",
    "    N = len(sample)\n",
    "    theta_estim = theta_func(sample)\n",
    "    \n",
    "    theta_asterisk_array = []\n",
    "    for _ in range(B):\n",
    "        bootstrap_sample = numpy.random.choice(sample, replace=True, size=N)\n",
    "        theta_asterisk = theta_func(bootstrap_sample)\n",
    "        theta_asterisk_array.append(theta_asterisk)\n",
    "    left_theta_asterisk, right_theta_asterisk = numpy.quantile(theta_asterisk_array, [alpha/2, 1-alpha/2])\n",
    "    left_bound, right_bound = 2 * theta_estim - right_theta_asterisk, 2 * theta_estim - left_theta_asterisk\n",
    "\n",
    "    return left_bound, right_bound"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "b10aa04e-4bb4-4394-8d04-132c0191fc16",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 238 ms, sys: 0 ns, total: 238 ms\n",
      "Wall time: 237 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(4.383626630619778, 4.851248249100453)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%time\n",
    "theta_func = lambda sample: numpy.percentile(sample, 75) \n",
    "bootstrap_ci(sample, theta_func, alpha=0.05)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c947c008-d5ce-4b65-a9ab-14595b019c21",
   "metadata": {},
   "source": [
    "Код рабочий, но у него есть минус: он очень долгий. Поэтому, чтобы ускорить работу, давайте генерировать не 1, а сразу `batch_size` выборок, чтобы ускорить работу.\n",
    "\n",
    "При этом, придется переписать функцию `theta_func`, чтобы она работала с массивом."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "5ec92bff-dd3c-4d5b-b20d-386456750089",
   "metadata": {},
   "outputs": [],
   "source": [
    "theta_func = lambda sample: numpy.percentile(sample, 75, axis=1) \n",
    "\n",
    "def fast_bootstrap_ci(sample, theta_func, alpha=0.05):\n",
    "    \"\"\"\n",
    "        Функция для построения доверительного интервала через бутстрап\n",
    "        \n",
    "        Параметры:\n",
    "            - sample: изначальная выборка\n",
    "            - theta_func: функция генерации оценки theta по выборке.\n",
    "                - Например, lambda sample: numpy.percentile(sample, 75)\n",
    "            - alpha: уровень значимости критерия. Доверительный интервал будет ширины 1-alpha.\n",
    "        Возвращает:\n",
    "            - левую и правую границы дов. интервала.\n",
    "    \"\"\"\n",
    "    \n",
    "    B = 2000 # Чтобы ускорить работу\n",
    "    batch_size = B // 20\n",
    "    N = len(sample)\n",
    "    # Добавляем размерность к выборке, чтобы работать с массивом массивов.\n",
    "    theta_estim = theta_func(numpy.expand_dims(sample, axis=0)).ravel()\n",
    "    assert len(theta_estim) == 1\n",
    "    theta_estim = theta_estim[0]\n",
    "    \n",
    "    theta_asterisk_array = []\n",
    "    for _ in range(0, B, batch_size):\n",
    "        # Генерируем сразу batch_size выборок\n",
    "        bootstrap_sample = numpy.random.choice(sample, replace=True, size=(batch_size, N))\n",
    "        theta_asterisk = theta_func(bootstrap_sample).ravel()\n",
    "        assert len(theta_asterisk) == batch_size\n",
    "        theta_asterisk_array = numpy.concatenate([theta_asterisk_array, theta_asterisk])\n",
    "    left_theta_asterisk, right_theta_asterisk = numpy.quantile(theta_asterisk_array, [alpha/2, 1-alpha/2])\n",
    "    left_bound, right_bound = 2 * theta_estim - right_theta_asterisk, 2 * theta_estim - left_theta_asterisk\n",
    "\n",
    "    return left_bound, right_bound"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "32f610b6-d72e-4186-81f6-880fb6be547c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 40.7 ms, sys: 0 ns, total: 40.7 ms\n",
      "Wall time: 39.9 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(4.383626630619778, 4.87087359274933)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%time\n",
    "theta_func = lambda sample: numpy.percentile(sample, 75, axis=1) \n",
    "fast_bootstrap_ci(sample, theta_func, alpha=0.05)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dbcc6ccc-eef7-4e6a-8125-2b6f23bdf78c",
   "metadata": {},
   "source": [
    "Результат не изменился, но время работы сократилось в 6 раз!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d4cd260b-84a6-4e95-be0f-cc41c362076b",
   "metadata": {},
   "source": [
    "А теперь самое время проверить наш бутстрап критерий! И снова с помощью Монте-Карло."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "0f3eaaa7-f8cc-48de-9c90-b1f4c8de8a75",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "5c82202b0d684728aa72cb175fc5a0be",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/1000 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "FPR: 0.056\n",
      "CI=(0.043374813385441996, 0.07202334814973096)\n"
     ]
    }
   ],
   "source": [
    "numpy.random.seed(42)\n",
    "\n",
    "bad_cnt = 0\n",
    "MC_size = 1000\n",
    "N = 5000\n",
    "alpha=0.05\n",
    "theta = example_dist.ppf(0.75)\n",
    "theta_func = lambda sample: numpy.percentile(sample, 75, axis=1) \n",
    "\n",
    "\n",
    "for i in tqdm(range(MC_size)):\n",
    "    # Генерирую выборку теста и контроля\n",
    "    ex_sample = example_dist.rvs(N)\n",
    "\n",
    "    left, right = fast_bootstrap_ci(ex_sample, theta_func, alpha=0.05)\n",
    "    \n",
    "    bad_cnt += 1 - (left < theta < right)\n",
    "\n",
    "\n",
    "print(f\"FPR: {round(bad_cnt / MC_size, 4)}\")\n",
    "print(f\"CI={proportion_confint(count = bad_cnt, nobs = MC_size, alpha=0.05, method='wilson')}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8fa85caa-e455-4d7f-bc7a-cb391320c42b",
   "metadata": {},
   "source": [
    "Видим, что критерий работает валидно (хоть и очень долго), поэтому теперь самое время решить изначальную задачу!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "b38444a7-e3de-4fda-aff4-371d6b2ae1d8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4.392414326845837, 4.864705982389839)"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample = numpy.load('bootstrap_example_1.npy')\n",
    "fast_bootstrap_ci(sample, theta_func, alpha=0.05)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2a6ccb52-f818-4ea7-85ea-b4ade75b4979",
   "metadata": {},
   "source": [
    "Да, отлично! Мы смогли посчитать доверительный интервал."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b69aa578-1cee-44c7-85a3-1e3badb1b632",
   "metadata": {},
   "source": [
    "### Промежуточные итоги про бутстрап\n",
    "\n",
    "Бутстрап &mdash; способ построения доверительного интервала для любой характеристики распределения, состоящий из 2 эвристик: \n",
    "- Замены истинного распределения на эмпирическое\n",
    "- Генерация итоговой выборки $\\theta^*$ с помощью Монте-Карло, чтобы корректно оценить квантили распределения.\n",
    "\n",
    "Это универсальный способ посчитать доверительный интервал для любых нетривиальных характеристик и любых распределений. И часто может пригодиться в работе, поэтому вы обязательно должны помнить про него.\n",
    "\n",
    "----\n",
    "\n",
    "## Основные вопросы про бутстрап:\n",
    "\n",
    "1. Когда бутстрап работает?\n",
    "    - Когда выборки достаточно большие. Обе эвристики, из которых состоит бустрап, работают если:\n",
    "        - $N$ достаточно большое. Тогда эмпирическое распределение лучше приближается к истинному и мы точнее оцениваем $\\Delta^*$.\n",
    "        - $B$ достаточно большое. Так мы точнее построим квантили распределения $\\Delta^*$.\n",
    "        - Первым параметром мы не всегда можем управлять, а вторым всегда.\n",
    "2. Можно ли генерировать бутстрап-выборки другого размера, нежели $N$?\n",
    "    - Нет, нельзя. Это следует из шага Монте-Карло, где мы пытаемся оценить $\\widehat{\\theta} - \\theta$, а $\\widehat{\\theta}$ построена по выборке размера N.\n",
    "3. Какого размера строит брать `B`?\n",
    "    - Рекомендация: `B = 10000`.\n",
    "    - Можно ли брать меньшего размера? Да, но надо проверять корректность с помощью Монте-Карло. Например, как мы сделали в примере выше.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f99d0ba1-2027-4798-a634-e351fa14eeea",
   "metadata": {},
   "source": [
    "  \n",
    "### Двуxвыборочный бутстрап\n",
    "\n",
    "Как с помощью бутстрапа построить доверительный интервал для разницы характеристик 2 распределений? Например, для разницы медиан в тесте и в контроле? Для этого надо повторить все те же шаги, что и для одновыборочного бутстрапа, но с модификацией: генерировать не 1, а 2 выборки сразу.\n",
    "\n",
    "Пусть у вас есть выборка $X,\\ Y$ размера $N, M$ соотвественно. Тогда:\n",
    "\n",
    "1. Считаем $\\widehat{\\theta_X}, \\widehat{\\theta_Y}$ по изначальной выборке. Считаем разницу между ними $\\widehat{\\theta} = \\widehat{\\theta_X} - \\widehat{\\theta_Y}$.\n",
    "2. В цикле размера `B`:\n",
    "    1. Генерируем из выборок `X` и `Y` новые выборки с возвращением размера `N` и `M` соответственно. \n",
    "    2. Считаем по этим выборкам $\\theta^*_{X, i},\\ \\theta^*_{Y, i}$. $\\theta^*_{i} = \\theta^*_{X, i} - \\theta^*_{Y, i}$\n",
    "3. Сохраняем $\\theta^*_1,\\ ...,\\ \\theta^*_B$ в массив.\n",
    "4. Строим доверительный интервал по формуле выше.\n",
    "\n",
    "Profit!\n",
    "    \n",
    "    \n",
    "-----\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0fa57875-f293-4343-a499-84824a98d2bf",
   "metadata": {},
   "source": [
    "\n",
    "## Виды доверительных интервалов в бутстрапе\n",
    "\n",
    "У бутстрапа есть 3 вида доверительных интервалов.\n",
    "\n",
    "1. Центральный: $CI = (2\\widehat{\\theta} - \\theta^*_{[1 - \\alpha/2]}, 2\\widehat{\\theta} - \\theta^*_{[\\alpha/2]})$. Его мы уже рассмотрели.\n",
    "2. Нормальный: $CI = (\\widehat{\\theta} \\pm z_{1-\\alpha/2}\\cdot \\sqrt{S^2_{\\theta^*}})$\n",
    "    - Если статистика $\\widehat{\\theta}$ распределена нормально (что на практике практически всегда так), то мы можем посчитать по выборке $\\theta^*$ стандартное отклонение $\\sqrt{S^2_{\\theta^*}}$. мы делаем предположение, что $\\sqrt{S^2_{\\theta^*}} \\approx \\sqrt{S^2_{\\widehat{\\theta}}}$ . Тогда центр распределения $\\theta$ будет лежать в данном дов. интервале.\n",
    "    \n",
    "3. Процентильный: $CI = (\\theta^*_{[\\alpha/2]}, \\theta^*_{[1 - \\alpha/2]})$\n",
    "    - Теоретически он работает, если существует некоторая монотонная функция $F$, такая, что $\\hat U = F(\\hat\\theta(X_i))$ и $\\hat U \\sim \\mathcal{N}(\\varphi, c^2)$, где $\\varphi = F(\\theta)$. Где $X$ &mdash; выборка, $ U$ &mdash; одно наблюдение случайной величины $\\hat U$.\n",
    "    - Док-во:\n",
    "        - Пусть $U^\\ast_i = F(\\theta^*_i)$, а $u^*_{[\\beta]}$ &mdash; оценка $\\beta$-квантили распределения $U^*$. Тогда по свойству монотонности $F: u^*_{[\\beta]} = F(\\theta^*_{[\\beta]})$.\n",
    "        - Оценки для квантилей случайной величины $\\hat U$ (помним, что $U$ &mdash; одно ее наблюдение) равны:\n",
    "            - $\\widehat{u_{[\\alpha/2]}} = U - z_{1 - \\alpha/2}c$ \n",
    "            - $\\widehat{u_{[1-\\alpha/2]}} = U + z_{1 - \\alpha/2}c$.\n",
    "        - Предположение бутстрапа: $u^*_{[\\beta]} \\approx \\widehat{u_{[\\beta]}}$.\n",
    "        - $$\\begin{align}\n",
    "            P(\\theta^*_{[\\alpha/2]} < \\theta < \\theta^*_{[1 - \\alpha/2]}) &=  P(F(\\theta^*_{[\\alpha/2]}) < F(\\theta) < F(\\theta^*_{[1 - \\alpha/2]})) \\\\\n",
    "            &= P(u^*_{[\\alpha/2]} < \\varphi < u^*_{[1 - \\alpha/2]})) \\\\\n",
    "            &\\approx P(\\widehat{u_{\\alpha/2}} < \\phi < \\widehat{u_{1 - \\alpha/2}} )) \\\\\n",
    "            &= P(U - cz_{1 - \\alpha/2} < \\varphi < U + cz_{1 - \\alpha/2})) \\\\\n",
    "            &= P(- z_{1 - \\alpha/2} < \\dfrac{U - \\varphi}{c} < z_{1 - \\alpha/2}) \\\\\n",
    "            &= 1 - \\alpha\n",
    "        \\end{align}\n",
    "        $$\n",
    "     - **На практике интервал работает практически всегда.**\n",
    "    \n",
    "### Сравнение интервалов\n",
    "\n",
    "Посмотрим на практике, насколько похожие значения они дают. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "ba1da154-aa12-418f-95a5-20d08b57a065",
   "metadata": {},
   "outputs": [],
   "source": [
    "def fast_bootstrap_ci(sample, theta_func, alpha=0.05):\n",
    "    \n",
    "    B = 1000 # Чтобы ускорить работу\n",
    "    batch_size = B // 20\n",
    "    N = len(sample)\n",
    "    \n",
    "    # Добавляем размерность к выборке, чтобы работать с массивом массивов.\n",
    "    theta_estim = theta_func(numpy.expand_dims(sample, axis=0)).ravel()\n",
    "    assert len(theta_estim) == 1\n",
    "    theta_estim = theta_estim[0]\n",
    "    \n",
    "    theta_asterisk_array = []\n",
    "    for _ in range(0, B, batch_size):\n",
    "        # Генерируем сразу batch_size выборок\n",
    "        bootstrap_sample = numpy.random.choice(sample, replace=True, size=(batch_size, N))\n",
    "        theta_asterisk = theta_func(bootstrap_sample).ravel()\n",
    "        assert len(theta_asterisk) == batch_size\n",
    "        theta_asterisk_array = numpy.concatenate([theta_asterisk_array, theta_asterisk])\n",
    "    left_theta_asterisk, right_theta_asterisk = numpy.quantile(theta_asterisk_array, [alpha/2, 1-alpha/2])\n",
    "    std = numpy.std(theta_asterisk_array)\n",
    "    \n",
    "    \n",
    "    central_left_bound, central_right_bound = 2 * theta_estim - right_theta_asterisk, 2 * theta_estim - left_theta_asterisk\n",
    "    percentile_left_bound, percentile_right_bound = left_theta_asterisk, right_theta_asterisk\n",
    "    norm_left_bound, norm_right_bound = theta_estim - norm().ppf(1-alpha/2) * std, theta_estim + norm().ppf(1-alpha/2) * std\n",
    "\n",
    "    return {\n",
    "        'central bootstrap': (central_left_bound, central_right_bound),\n",
    "        'percentile bootstrap': (percentile_left_bound, percentile_right_bound),\n",
    "        'norm bootstrap': (norm_left_bound, norm_right_bound)\n",
    "    }"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "84317443-7343-4200-87d7-20fd9f728c6a",
   "metadata": {},
   "source": [
    "Проверим, насколько корректны дов. интервалы через Монте-Карло. FPR будет отражать, в скольких процентах случаев истинное $\\theta$ не попал в доверительный интервал."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "21fd2672-49c5-4536-82e9-63c605307cfb",
   "metadata": {},
   "outputs": [],
   "source": [
    "def mc_result_dict_creator(bad_cnt, MC_size):\n",
    "    # Создает словарь, в котором значения по умолчанию инициализируются словарем\n",
    "    mc_result = defaultdict(dict)\n",
    "    for method in bad_cnt:\n",
    "        fpr = bad_cnt[method] / MC_size\n",
    "        left_fpr, right_fpr = proportion_confint(count = bad_cnt[method], nobs = MC_size, alpha=0.05, method='wilson')\n",
    "        mc_result[method]['FPR'] = fpr\n",
    "        mc_result[method]['FPR, left_bound'] = left_fpr\n",
    "        mc_result[method]['FPR, right_bound'] = right_fpr\n",
    "    return mc_result\n",
    "\n",
    "def mc_bootstrap_checker(N, example_dist, theta, theta_func, alpha=0.05, MC_size = 1000):\n",
    "    numpy.random.seed(42)\n",
    "    \n",
    "    # Создает словарь, в котором значения по умолчанию инициализируются 0\n",
    "    bad_cnt = defaultdict(lambda: 0)\n",
    "    for i in range(MC_size):\n",
    "        ex_sample = example_dist.rvs(N)\n",
    "\n",
    "        curr_res = fast_bootstrap_ci(ex_sample, theta_func, alpha=alpha)\n",
    "\n",
    "        for ci_type in curr_res:\n",
    "            left, right = curr_res[ci_type]\n",
    "            bad_cnt[ci_type] += 1 - (left < theta < right)\n",
    "    \n",
    "    return mc_result_dict_creator(bad_cnt, MC_size)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "d15a04b0-9abb-446b-b93f-e02c362a18c5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "5ae714b44624428eb2dc224ed4837543",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/6 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N_to_check = [50, 100, 500, 1000, 2000, 5000]\n",
    "\n",
    "example_dist = stats.expon(scale=5)\n",
    "theta = example_dist.ppf(0.5)\n",
    "theta_func = lambda sample: numpy.percentile(sample, 50, axis=1) \n",
    "\n",
    "final_results = {}\n",
    "for N in tqdm(N_to_check):\n",
    "    final_results[N] = mc_bootstrap_checker(N, example_dist, theta, theta_func, alpha=0.05, MC_size = 1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "ab89f17a-2b52-4b9b-81fa-6a71b2ab9966",
   "metadata": {},
   "outputs": [],
   "source": [
    "def show_FPR(result_dict, methods, colors):\n",
    "    pyplot.figure(figsize=(18.5, 8))\n",
    "    pyplot.title('Зависимость FPR от размера выборки для разных методов', fontsize=15)\n",
    "    N_array = list(result_dict.keys())\n",
    "    x_ticks = numpy.arange(0, len(N_array))\n",
    "\n",
    "    pyplot.hlines(0.05, x_ticks[0], x_ticks[-1], \n",
    "                   color='red', linestyle='-', label=\"$\\\\alpha$\")\n",
    "    for method, color in zip(methods, colors):\n",
    "        FPR = []\n",
    "        left_bound = []\n",
    "        right_bound = []\n",
    "        for N in result_dict:\n",
    "            curr_dict = result_dict[N][method]\n",
    "            FPR.append(curr_dict['FPR'])\n",
    "            left_bound.append(curr_dict['FPR, left_bound'])\n",
    "            right_bound.append(curr_dict['FPR, right_bound'])\n",
    "\n",
    "        pyplot.plot(x_ticks, FPR, color=color, label=method)\n",
    "        pyplot.fill_between(x_ticks, left_bound, right_bound, \n",
    "                   color=color, alpha=0.2)\n",
    "\n",
    "    pyplot.legend(fontsize=15)\n",
    "    pyplot.xticks(x_ticks, N_array)\n",
    "    pyplot.xlabel('N', fontsize=15)\n",
    "    pyplot.ylabel('FPR', fontsize=15)\n",
    "    pyplot.grid(linewidth=0.2)\n",
    "\n",
    "    pyplot.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "724e2818-3e58-4133-a7a5-7586904384b2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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kwZwiYnN3HJugLKjlVhr2/4aLyf952kTJkibFrZ9/wyYWVxdyrCjs58fXZ2IPnl0X3T9nH2FbmRQ1yLWISJlSSxMRkbJTB/vH4n+wfwQa7Le1T2C/2XQ2OY7EPlC/ju32cC2224MvTbHdGZwtTS4n/0wF/3AcL7WAY7yGTYisxTbT/wM7lkVt7IwSxT2Ou1TsbAeZ5G/iDvbbw0XAm9j7sh87Jkt78loZ5GIfot53LIuw96yX4+eSdCWo6Ti289vK2/D8Brm8vYjtnnUn9oHVl1ex92IV9hvt88ibinrZGYghwxHHediHpyews/I4Z4lZj20dMxdbD0Kw31gf9DrOh9gHtyPYB+l/Yx+SfT1QfoP9Fn6Xj9fAtoR4ADtr0CvYcXMaYFt4HMHWVac62DER5jrO+wJ2DA/nt9SRwKPYh7392IRJmwLO60soeS1Nxjiux/0hs7h1ymDv83Tst+qR2M/Gg9gWLJmOchOxD+WfYB+0Q7Dv+yryJx36OI75HfbBtTd5M7D48hL2AfUNPKd1bY5NpHjPWFKYi7Cf2wzs/XB2HbzY8e//Yd+DJti60MkRb2FmYq+9NDNeFXYvUrAP22OxCYZc7LgtKdjxZJwmYevaXmxi+BlsK42ikj2+BJHXHacptvvMNnz/HpyIvU9/xSYH7sYmVe8m/7TBBRnjKLumgNefwiYwcrEtr1KxyaC+2FZYe4p5nuLUz27Yrps/O14PcWxvik1gdcb+XknE/v/2PHlJpgHYMUu862Jtx37Oz9kd+Pd3t4iIkiYiImUoDZvQGIB9QD0X+4f6LOzDnvPh6QvsH8KPYBMJP2KbmPv643aoY8nGPsy+gv1j1N0BYHYhcR3F9oef4ti3Bvbh4eUSHsdbUUmNEdg/usdim+Nvx16n+7eWH2Dvy3PYP/id35wWNYiqt47YRI1x7LsaO/6Lv/yAfch5Atv6wtf0zUeBntiWPYuw3Qe+wMZ96gzEkI5Nlk3HJsl2YR9anE3n47AP2q9gvzHfi01oPOV1nEBsMqM+ttvWJ+Qf/8PJUPg30JnYax6PfeBu7DjmT+TvrjEN2/VjkSOGd7BJCKfx2ISAc1Daj7FJlM8KOb+7bxz/pmAfFvvg2d2oJHVqhiPGkY7lD2z3AvfP6g7HOV5yxHrccW3e9xvs1M6jHOdLxHY/Kaw7y0ns520ttkufs6uG870rbncQsMmpGx0/+3pQ/xj7HnbCPuT2xz5YF2QweeM6FTSNeWGKuhdDsb+3FmKTVm9if/c+7FYmBXufQ7D3fRN20OfijNnirR55AxwnYj/rj/so19UR8z/I+8x9j02Wvo5toRfrYz9vhyi8xcg6bLeifwP/xSZ1DmC7m5Xk+opTP9/DdiVtje+E04/kDZ47Fvv/1oPYz/k+bBLZe1yW9o793D9n6pojIn4VYExp/r8SERGRSiQc+9DYsIhyFZXBJhXf9Hcg5ew6bKLiMvK6IZW3BdjBpsMLeD0G21Li2zKO4zr8fy/EUwwFv/etsLNiFTTjkIhIpaGWJiIiIiJSkP0UPqPVFgof9FXOXoW99yexXeVERCo9JU1EREREpCCFTTcOGqSzKivsvT9M3vg3IiKVmrrniIiIiIiIiIj4oCmHRURERERERER8UNJERERERERERMSHKjumydGjR82BAwf8HUaJBQUFAZCTk+PnSETKluq6VCWq71KVqL5LVaL6LlVFZa/rV1999THgAl+vVdmkyYEDBwgNDfV3GCUWHBwMQFJSkp8jESlbqutSlai+S1Wi+i5Vieq7VBWVva4bYwpsUaHuOSIiIiIiIiIiPihpIiIiIiIiIiLig5ImIiIiIiIiIiI+KGkiIiIiIiIiIuKDkiYiIiIiIiIiIj5U2dlzREREREREKqM6derQqFEjqlev7u9QRAAIDLTtMRo3buznSPLLysoiPj6e1NTUUu2vpImIiIiIiEglUadOHRo3bszBgwfJyMjwdzgiAAQFBQGQk5Pj50jyq1WrFs2aNQMoVeJE3XNEREREREQqiUaNGilhIlICGRkZHDx4kEaNGpVqfyVNREREREREKonq1asrYSJSQhkZGaXuzqakiYiIiIiIiIiID0qaiIiIiIiIiIj44I+kyY3AbmAf8LSP10cDvwLbgNVAS7fXwoC9jiXMbftVwHbHMf8DBJzxqEVERERERESkSinvpEkQMAPoA3QAhjj+dbcFuBq4HFgKTHFsrw+MA64BOjl+Dna89hYwAmjrWG4ssysQERERERGRSqF3796MHDnyjB6zZcuWGGPo27fvaZU5k6pXr864ceO44oorSrRf27ZtGTduHHXr1i2jyCq/8k6adMK2BvkNOAUsBvp5lVkDpDt+Xg+EOH7+GxAJJAJJjp9vBJoC5zvKGmAhcGuZXYGIiIiIiIhUCjfccAOjRo3ydxhl7pxzziE8PJwrr7yyRPu1a9eO8PBw6tWrV0aRVX7Vyvl8zYA/3NZjsS1HCnIv8GUh+zZzLLE+thcqKCiI4ODgoopVOKrMUlWorktVovouVYnqu1QlZVHfAwMDCQoKOuPHPVsFBtp2AkXdM+d9zcrKKvKYzmMFBQUVeNzilDmTnOcoaf0oSZw1atTg5MmThR6nIgsMDCxVDqAiDwR7J7abztQzeMz7gE3ApoYNG57Bw4qIiIiIiEhx/eUvf+Hrr78mOTmZhIQEVq9e7dFKonnz5rz//vvEx8dz/PhxvvjiC9q1a+d6vWXLlmRnZzNw4EBmzpxJQkICMTExjBs3joAAO8Tl2LFjGT16NK1atSI7O5vs7GzeeecdAN555x3Wr1/PLbfcwi+//EJaWhrXXHMNTZo0Ye7cuezZs4fU1FR+/fVXxo8fX+rpauvUqcOCBQtISkri0KFDvPDCC/nK9OzZkx9++IETJ05w8OBBpk+fTu3atT3KtGrVimXLlpGYmEhSUhKffPIJF110kev1lJQUAObNm+e61pYt7fCgY8aMYdeuXa7jr1ixgsaNG9OjRw+WL18OwP79+8nOzmbfvn0A3HXXXWRnZxMaGsrq1atJTU3liSeeAOCll15iy5YtJCcnExMTw8KFC2ncuLFHvPv27WPKlCk899xzxMbGkpyczMKFCzn//PNLdR/9qbxbmhwEmruthzi2ebseeA7oAThTWQeB67z2/daxPcRru69jAsxxLMTFxZmkpKQSBV+RVObYRUpCdV2qEtV3qUpU36UqOZP1vXHjxuTk5Jyx4/lDjx49+Oqrr1izZg1hYWGkpaXRtWtXmjRpQk5ODsHBwXz33XckJCTwwAMPkJ6eztNPP82qVato164dmZmZrnswadIkli1bxsCBA/nrX//KCy+8wPbt21myZAlz5szhoosuolevXvTv3x+Ao0ePkpOTgzGGVq1aMWnSJMaPH8+RI0fYt28fwcHBJCQkMHr0aJKSklzdVxo0aMADDzwA4Dp3Tk5Oge+Fc/vkyZP5/PPPGThwIN27d+eFF14gPj6emTNnAtChQwdWrFhBZGQkt912G82bN2fSpEm0bt2aPn36ALbrzVdffUVWVhYjRowgOzubf//733zzzTdcdtllJCUl0bNnT9asWcOECRNYsWIFALGxsQwdOpSnn36aMWPGsGPHDho0aECvXr2oWbMmGzdu5PHHH2fatGn079+fw4cPc/LkSXJycsjNzQXgvffeY+bMmYSHh5OcnExOTg4NGzbkpZde4tChQ1xwwQU8/vjjrFy5kiuuuMLjftx+++3s27ePESNG0LRpU6ZMmcLs2bMZPHjwGa1PxZWbm1u6z6IxpjyXasaY34wxrY0x5xhjfjHGdPQq83/GmP3GmLZe2+sbY6KNMcGOJdqxDWPMT8aYzsaYAGPMl8aYm4qKZePGjQY7BkqlWoKDg01w02C/x6FFS1kvwcHBJjhYdV1L1VhU37VUpUX1XUtVWsqivrdv3z7/9tcwrPHT8lrJr+GHH34whT2PjR8/3hw7dszj3tWrV88kJyebhx56yACmZcuWxhhj3n33XY99t2zZYhYtWuRanzp1qomOjs53jvnz5xtjjLniiisKjTUoKMgMGTLEZGRkmOrVq3ucu2/fvgXu5yyzatUqj+1z5swxsbGxJiAgwABm0aJFZs+ePSYwMNBVZtCgQcYYYzp37mwAc//995usrCzTunVrV5lmzZqZkydPmqefftoApnbt2sYYY8LCwjzON336dLN06dIC4+zbt68xxpiWLVt6bA8LCzPGGPPoo48Wen8CAwPNhRdeaIwx5rrrrnNtj46ONgkJCaZ27dqubUOHDjU5OTm+63A5LIWd1xizqaDcQXl3z8kGHgZWATuBj4AdwHjgFkeZqcB5wBJgK/CpY3siMAHY6FjGO7YBPAS8jR1kdj9546CcfWpjOy21QBMri4iIiIhIpXLuuedyzTXX8O677xZY5vrrrycyMpLjx4+7xtpITU1l8+bNXH311R5lv/rqK4/1X3/9lZCQEIojNjaWX375Jd/2kSNHsmPHDtLT08nOzuaDDz6gZs2atGjRoljHdRcREeGx/vHHH9OsWTNXjJ06dSIiIsLVsgNg2bJlZGVl0a1bN1eZn3/+mejoaFeZgwcP8v3337vKFGTr1q3cdNNNhIeHExoa6hrjpbicrVbc3XjjjXz//feulicHD9qOHm3btvUoFxkZSVpamms9IiKCwMBAQkNDSxSDv5V39xyALxyLu7FuP19fyL7zHIu3TcClpxlX5VEdO1FzY2zKKb3w4iIiIiIichZ7zN8BFF9wcDCBgYEcPny4wDINGzakS5cu3HHHHfle+/rrrz3Wk5OTPdZPnTpFzZo1ixVLXFxcvm2jRo1i6tSpTJ48me+++46kpCRCQ0OZOXNmsY/rLj4+3ud606ZN+eOPP2jatGm+OHJzc0lISKB+/fqusr5ijYuLc41bUpB58+ZRp04d7rvvPsaNG8exY8eYNWsW48aN80jUFMT7vFdffTWffvopERERTJo0ifj4eIwxbNiwId/98b72jIwMUlNTadq0aZHnrUj8kTSR05ULxAN1gK7ArxQ8iouIiIiIiEgFkZSURE5OTqEPzomJiSxfvpwJEybkey01NfWMxWKMybdt0KBBLF26lOeff961rUOHDqU+R6NGjXyuO5NGhw8fzlcmMDCQBg0akJiY6CrTsWPHfMdu3Lixq0xBjDG8/vrrvP7664SEhDBs2DBefPFFYmNjmT17dpHxe9+j/v37c/ToUW6//XbXtoJa4HhfV61atahTp06hCbOKqCLPniNFSQVSgMuAq4CSJz5FRERERETKTXp6Ohs2bOCuu+4qsMzq1avp2LEjO3bsYPPmzR7Lnj17SnS+krQ8Aftg7z2t7rBhw0p0TnfOAWidBgwYwKFDh4iNjQVgw4YN9O/f36PbzIABA6hevTrr1q1zlbnqqqto1aqVq8yFF17Itdde6ypz6tQpgEKvNTY2lsmTJ7Nv3z5XIqg4+7mrVatWvmmZC7o/vXv39pgFqH///uTm5rJp06ZinauiUEuTyi4b2+qkLtAN212nciXuRERERESkCnn66af5+uuv+fLLL5kzZw5paWl06dKFTZs2sWLFCl599VXuvPNOvvnmG6ZPn87BgwddU+SuW7eOxYsXF/tcu3btokmTJoSFhREVFcWxY8c4cOBAgeUjIyN59NFH2bBhA/v372fYsGG0adOm1NfasWNHZs2axbJly+jevTv33nsvI0eOdLXgmDhxIlu2bOGTTz7hrbfeIiQkhMmTJ7Ny5UrWr18PwIIFCxgzZgxffvklY8eOJScnx9XVxtlaJCsri99++43BgwcTFRVFZmYm27ZtY/r06SQmJrJ+/XpSUlLo2bMnbdu2ZcyYMQDs3r0bgPvvv5/FixeTnp5OVFRUoffnscce47XXXuOzzz7j2muv5c477/RZNiMjgxUrVjB16lSaNm3K1KlTiYiIYOfOnaW+n35RzrPnVJil0s6eExJsgm8NNvyZ/EsnDH0wXIGhhv9j1aLldBbNrqClKi2q71qq0qL6rqUqLeU2e04lXLp3726+++47k5aWZpKSksw333zjMZNN06ZNzbx588yRI0dMZmamiY6ONv/9739Nhw4dDBQ8g838+fM9ZuapUaOGmTdvnomLi8zISyMAACAASURBVDPGGDN//nyf5ZxL7dq1zbx580xCQoJJSEgwc+fOdc0w07Fjx0LP7b44ywwdOtR88MEH5vjx4yY+Pt6Eh4fnK9urVy+zfv16k5GRYeLi4syMGTM8Zp0BTOvWrU1ERIQ5fvy4SU1NNZ999plp06aNR5nevXubX375xWRkZLhmxAkLCzPr1q0zCQkJJi0tzfzyyy/mn//8p8d+o0ePNjExMSYrK8s105Bz9hzvOADz5JNPmt9//92cOHHCREZGmjZt2hhjjHnkkUdcZaKjo80rr7xixo0bZ44cOWJOnDhhPvjgA1O3bl2/1bnSzp4T4KsfV1WwadMmU9lG7QUIDgmGqyHp90Lml66L7Xi1DThaToGJnGHBwcEApZtLXaSSUX2XqkT1XaqSsqjv7du3Z9euXWfseCJnQlBQEAA5OTkAREdHs3TpUp588kl/huWhsM+OMWYzdp7afDSmydkoBTiBfcsvxc62IyIiIiIiIiIloqTJ2SoLiAOaYMc6aeDfcEREREREREQqGw0Ee7ZLBGoAocABYC928FgRERERERGRMtC6dWt/h3DGqKVJVXASO8NOCNAVCPZvOCIiIiIiIiKVgZImVUkCttvONUA7IMi/4YiIiIiIiIhUZOqeU9VkYluetAQaYWfYOe7XiEREREREREQqJLU0qYoMttUJwLXARagmiIiIiIiIiHjRo3JVlg4cA9oAnYHz/BuOiIiIiIiISEWipElVlwscxY5v0g1oAQT4NSIRERERERGRCkFJE7HSsK1OOgCdgHP9G46IiIiIiEhlMGLECPr165dve3R0NFOnTnWtz58/n40bN572+cLCwjDGULt27dM+VnG0bduWcePGUbdu3RLt17t3b0aOHFlGUZUfJU0kTy52auKa2FYnzfwbjoiIiIiISEV33333ceutt+bb3r9/f/7zn//4IaIzq127doSHh1OvXr0S7XfDDTcwatSoMoqq/Gj2HMkvFcgALgOaAL861kVERERERCqwatWqkZubS25urr9DYevWrf4OoVIIDAwkKCiIrKwsf4fik1qaiG/Z2FYn52NbnTT1bzgiIiIiInJ2cHZT6devHzt37iQjI4O1a9dyySWXeJQLCAhgzJgx7N27l8zMTHbv3s1dd93lUWbNmjUsWbKEESNGsG/fPjIzM7nwwgsBGD58ONu2bSMjI4MjR46wZMkSzj//fNe+3bp149tvvyUtLY1jx44xZ84czjsvb3YMZzeYSy+9lK+++ooTJ06wc+dO+vfv73H+q6++mrvvvhtjDMYYwsLCgPzdc3xp3rw5ixYtIiEhgbS0NFauXEm7du2KdR8vueQS/ve//5Gens7u3bt9tnb517/+xZ49e8jMzGTv3r0+W3707NmT9evXu+7TjBkzXF1/evToweeffw5ATEwMxhiio6MBqFu3LnPnzuXgwYOcOHGC3377jTlz5gAwbtw4nnjiCVq1auW6L/Pnzwc83/+oqCgyMzO55ppraNKkCe+88w779+93XdOECROoXr26K9aWLVtijGHIkCEsXLiQ48ePExcXx9ixY4t1z0pDSRMpXIpjuQK4Eqjh33BERERERKTya9myJa+++ioTJkxg6NCh1K1bl1WrVlGjRt4Dx/Tp03n++eeZM2cOffv2JSIignnz5tG3b1+PY3Xt2pUHH3yQMWPG8Pe//52UlBSee+45Zs+ezXfffcett97Kgw8+SEpKiispcu211/L1119z5MgRBg4cyKhRo7jppptcD/buPvjgAz799FP69+/P3r17Wbx4Mc2a2bEMHnroIXbu3MmKFSvo3LkznTt3ZsWKFcW6B8HBwaxbt46LL76YBx54gMGDB1O7dm2+/vpratasWeT+H374IcuXL2fAgAFs376dJUuWcPnll7teHz58OG+++Saffvopf//731myZAnTpk1jzJgxrjIdOnRg5cqVHDt2jNtuu41x48YxdOhQli5dCsDPP//M448/DtjuRp07d3YljV599VW6devGY489xk033cTzzz+PMQaAt99+m/fff5/Dhw+77suECRNc523VqhVTpkzh5Zdfpk+fPkRHR9OwYUMSExMZPXo0N954I1OnTuWee+5h+vTp+a596tSppKenM3DgQObOncu4ceN46KGHinXfS8yZ9alqy8aNGw1Q6ZbgkGATfGuw4c+U/9ITw18xNPL/fdBy9i/BwcEmODjY73Fo0VIei+q7lqq0qL5rqUpLWdT39u3b+/26TneZP3++McaYLl26uLa1aNHCZGVlmfvvv98A5qKLLjI5OTnmrrvu8tj33XffNT/99JNrfc2aNSY9Pd00atTIta1u3bomLS3NTJs2rcAY/ve//5lvvvnGY1vPnj2NMcZ07NjRACYsLMwYY8w999zjKlO/fn2POAGzceNGM3/+/HzniI6ONlOnTvW4bvfn0PHjx5tjx4551JF69eqZ5ORk89BDDxUYuzOuZ555xrUtICDA7Ny50yxatMi1Hhsba+bNm+ex74wZM0xycrKpUaOGAcyiRYvMnj17TGBgoKvMoEGDjDHGdO7c2QCmb9++xhhjWrZs6XGs7du3m4cfftgAJigoyAQFBXm8PnXqVBMdHV3g+3/FFVcUWk+CgoLMkCFDTEZGhqlevboBTMuWLY0xxqxatcqj7Jw5c0xsbKwJCAgo1WfHGLOpoNyBxjSR4ksBqgN/BmKBPcApv0YkIiIiIlLlvfbaa1x55ZV+OffWrVt57LHHSrxfXFwcP/74o2v9999/Z/PmzXTq1InZs2fz17/+ldzcXCIiIggKCnKVW716NUOGDCEwMNA1bsnmzZuJj493lenSpQvnnnuuz1YjALVq1aJLly488sgjHsdet24dp06d4qqrrmLHjh2u7V999ZXr58TEROLj4wkJCSnxNXu7/vrriYyM5Pjx4644UlNT2bx5M1dffXWR+0dERLh+NsawfPlyBg0aBEBISAjNmjVjyZIlHvt8+OGHPPTQQ1x22WVs2rSJTp06sXTpUo8xYJYtW0ZWVhbdunVj/fr1BZ5/69atPPnkk+Tk5LBmzRr27t1b7GuPjY3ll19+ybd95MiR3HfffbRu3ZpatWq5trdo0YL9+/f7vHaAjz/+mBEjRhASEsIff/xR7DiKQ91zpGSysGOdNAa6Ag38G46IiIiIiFQ+7kkO921Nm9rBFBs2bEi1atU4fvw42dnZruXdd9+levXqrnJgEzDuGjSwDymHDx/2ee7g4GCqVavGW2+95XHsU6dOcc4559C8eXOP8snJyR7rp06dKlb3maI0bNiQO+64wyOG7OxsevXqlS8GX7zvofv9c/7rfW+c6/Xr13eV8y6Tm5tLQkKCq0xBHn74YT755BPGjh3Lzp072blzJ7fffnuRcfuKC2DUqFG88sorRERE0K9fP0JDQ11dbrzvt69rd17PmaaWJlI6SdjxTToBMcBe7OCxIiIiIiJSrkrT0sPfGjVq5HObs4VHYmIiWVlZdO3a1edMOO4Pzc5xNJwSEhIA+wDt/NldcnIyubm5hIeH88UXX+R7/dChQyW7mFJKTExk+fLlHmN9OKWmpha5f6NGjUhMTPRYdyaKnP963+fGjRu7zu0s510mMDCQBg0aeBzbl5SUFEaOHMnIkSO58soreeKJJ3j//ffZtm0bO3fuLHRf7/cMYNCgQSxdupTnn3/eta1Dhw4+9/eO2bleUKLsdKiliZTeSSAOCMHOsBPs33BERERERKRyaNy4MV26dHGtN2/enD//+c/89NNPAHzzzTcEBQVRt25dNm/enG8pbHraH3/8kfT0dNcsNt7S09NZv349F198sc9jl/TBu7QtT1avXk3Hjh3ZsWNHvhj27NlT5P7us/gEBATQr18/1/2LjY3l4MGDru46ToMHDyYlJYXt27cDsGHDBvr3709gYF5qYMCAAVSvXp1169a5rg/yt/Zwt337dsaMGUNQUBDt27d37VeS+1KrVi1OnjzpsW3YsGE+y7pfuzPmQ4cOERsbW+zzFZdamsjpSwBqAp2B/Y4lx68RiYiIiIhIBXb06FHee+89nn/+eTIyMvj3v/9NfHw8CxYsAGDPnj3MmjWLxYsXM2XKFDZt2kTNmjXp2LEj7dq1Y8SIEQUeOyUlhQkTJvDiiy9yzjnn8MUXX1CjRg369u3Lv//9bw4dOsRTTz3F6tWryc3NZenSpaSmptKiRQv69u3Lc889V6LxOXbt2sXf/vY3brjhBhISEoiOji6ylQbY2WfuvPNOvvnmG6ZPn87Bgwdp3LgxPXr0YN26dSxevLjQ/YcPH86pU6eIiopi+PDhtGnThiFDhgC2JUd4eDizZ88mISGByMhIevTowYMPPsizzz7rSk5MnDiRLVu28Mknn/DWW28REhLC5MmTWblypWs8k927dwNw//33s3jxYtLT04mKimLt2rVEREQQFRVFYGAg9957LydOnHAlbnbt2kWTJk0ICwsjKiqKY8eOceDAgQKvJzIykkcffZQNGzawf/9+hg0bRps2bXyW7dixI7NmzWLZsmV0796de++9l5EjR/pswXLa/D2LjWbPKdni19lzilquwtAbQzcMdf1/r7RU7kWzK2ipSovqu5aqtKi+a6lKi2bP8b04Z5Hp37+/2b17t8nMzDTr1q1zzVrjvowcOdJERUWZzMxMEx8fb7799lvzj3/8w/X6mjVrzJIlS3ye57777jM7duwwmZmZ5vDhw+bDDz80derUcb3eqVMn8+WXX5qUlBRz4sQJs2PHDjNt2jRz/vnnG8ibpaZ27doex/WeFad169YmMjLSJCcnG2OMCQsL81nOe/YcwDRt2tTMmzfPHDlyxGRmZpro6Gjz3//+13To0KHA++eMKzQ01Kxbt85kZGSYPXv2mAEDBuQr+/DDD5u9e/eakydPmv3795tRo0blK9OrVy+zfv16k5GRYeLi4syMGTPyXfPo0aNNTEyMycrKcs2IM2XKFLNt2zZz/Phxk5SUZNasWWO6devm2qdGjRpm3rx5Ji4uzhhjXDMM+boPgKldu7aZN2+eSUhIMAkJCWbu3LmumXucdcM5e87QoUPNBx98YI4fP27i4+NNeHj4aX12Cps9J6BMMjGVwKZNm0xoaKi/wyix4JBguBqSfk/ydygFqwXUwY5zEg3k74IoUqTgYNvfKympAtd1kTNE9V2qEtV3qUrKor63b9+eXbt2nbHj+cP8+fO59NJLqYzPY+Kbc/afnJyy7XLQsmVLYmJiuPnmm1mxYkWJ9i3ss2OM2Qz4nLJI3XPkzMsAMoGLsLPsbAeKHsdIREREREREpELRQLBSNgxwDAgCrgVaAQH+DEhERERERESkZNTSRMpWGrblycXYVidRjm0iIiIiIlIl3XPPPf4OQSqpAwcOEBBQvt/Gq6WJlL1c4ChQA+iKnaJYrU5ERERERESkglPSRMrPCSAJuBT4M3bAWBEREREREZEKSkkTKV85QDx2dp1uQFP/hiMiIiIiIiJSECVNxD+OAynAFcD/YbvuiIiIiIiIiFQgSpqI/2RjW53UA/4CNPJvOCIiIiIiIiLulDQR/0sBUoGrgMuAc/wbjoiIiIiIiAgoaSIVRRYQh21t0hVo6N9wRERERERERJQ0kYolCcgEQoEOQDX/hiMiIiIiIlVbWFgYxhhq165dLudr27Yt48aNo27duiXar3fv3owcObKMoqq6lDSRiuckttXJhdgZdoL9G46IiIiIiEh5adeuHeHh4dSrV69E+91www2MGjWqjKKqupQ0kYorETgFdAYuBoL8G46IiIiIiFRs1apVIzBQj7mFCQwMpHr16v4Oo9JQbZKKLRM7w04L4FqgZC3URERERESkgpk/fz4bN27k+uuv55dffuHEiROsXbuWDh06eJSrVasWb7zxBocPHyYjI4OffvqJ3r17e5RZs2YNS5YsYcSIEezbt4/MzEwuvPBC1/a7776b3377jdTUVBYuXMg555xDaGgoGzZsIDU1lTVr1tC8efNixX3JJZfwv//9j/T0dHbv3s2tt96ar8y//vUv9uzZQ2ZmJnv37vXZ8qNnz56sX7+ejIwMjhw5wowZM1xdf3r06MHnn38OQExMDMYYoqOjAahbty5z587l4MGDZGRkcODAAebMmQPAuHHjeOKJJ2jVqhXGGIwxzJ8/3+N+9+vXj6ioKDIzM7nmmmto0qQJ77zzDvv373dd04QJEzwSKi1btsQYw5AhQ1i4cCHHjx8nLi6OsWPHFuuenQ00YoRUfAZIAGoBXYC9QDSQ68+gRERERESktFq0aMHUqVN58cUXycjI4JVXXuHDDz/ksssuc5WZO3cut9xyC88++yz79u1jxIgRrFixgp49e/L999+7ynXt2pWLLrqIMWPGkJ6eTkpKCgCdO3emYcOGPPLII7Ro0YLXXnuNjIwMrrnmGqZMmUJaWhr/+c9/mDNnDn369Cky5g8//JCZM2fy0ksvMXz4cJYsWcJVV13Ftm3bABg+fDhvvvkm06ZNY9WqVfTs2ZNp06ZRo0YNJk+eDECHDh1YuXIlkZGR3HbbbTRv3pxJkybxpz/9iT59+vDzzz/z+OOPM23aNPr378/hw4c5efIkAK+++irXXnstjz32GEeOHKF58+Z0794dgLfffpu2bdvSq1cv+vfvD8DRo0ddsbdq1YopU6Ywfvx4jhw5QnR0NA0bNiQxMZHRo0eTlJTk6hZ0wQUX8MADD3hc+9SpU/n8888ZOHAg3bt3Z9y4cRw7doyZM2eW+L2vbJQ0kcojA9vy5CKgMbAdO1WxiIiIiEiV9hpwpZ/OvRV4rMR71a9fn65du7Jv3z7Adhn55JNPuPjii9m9ezft27dnyJAh3HPPPSxcuBCAVatWsW3bNl544QVuvPFG17Hq1avHlVdeSXx8vMc5zjvvPPr168fx48cBuO6667jvvvvo3r07a9euBeDCCy9k5syZ1KpVi4yMjEJjfvvtt5k2bZorll9//ZVnnnmGIUOGEBAQQHh4OPPnz+eJJ54AIDIykrp16/LMM8/w+uuvc/LkSV544QUOHDjALbfcQm6u/RY4MTGRjz76iM6dO7N+/Xp2794NwJYtWzhw4IDr/J06dWLGjBl89NFHrm3vv/8+AAcPHnQlWDZs2JAv9oYNG7pa9jgdPHiQJ5980rX+/fffk5aWxrx583jkkUfIyspyvbZjxw5XIuWrr76iUaNGPPvss7z11lsYYwq9b5WduudI5WKAY9jxTboCrYAAfwYkIiIiIiIlFRMT40qYAPz6668AhISEABAaGkpgYCBLlixxlTHGsGTJErp16+ZxrM2bN+dLmABs2rTJlTAB2LdvHydPnmTdunUe28AmT4oSERHhEcvy5cvp1KmTK+5mzZp5xAu2dUrdunVdLWg6depERESEK2ECsGzZMrKysvJdl7etW7fy5JNP8uCDD9K2bdsi43UXGxvrkTBxGjlyJDt27CA9PZ3s7Gw++OADatasSYsWLQq8doCPP/6YZs2aud6vs5lamkjllIZteXIxttVJlGObiIiIiEiVU/KWHv6WnJzssX7q1CkAatasCUDTpk1JTU3N1/ojLi6O2rVrc84557j2iYuLK/Y5UlNTPVpGeJ+3MN6Jmfj4eJo2beqK11cszvX69eu7ynmXyc3NJSEhwVWmIA8//DDjx49n7NixzJw5k7179/LCCy/w4YcfFhm7r3s0atQopk6dyuTJk/nuu+9ISkoiNDSUmTNn5rsfvq7deT1//PFHkeevzNTSRCqvXOAoUAM7NXFz1OpEREREROQscPjwYerUqUOtWrU8tjdu3Ji0tDRXsgMot+4hjRo1yrd++PBhANe/3mUaN24M2C44znLeZQIDA2nQoIGrTEFSUlIYOXIkTZs25fLLL2fDhg28//77XHLJJUXG7useDRo0iKVLl/L8888TGRnJpk2bSEvz/U20r2t3Xs/ZTkkTqfxOYKcn7ghchR0wVkREREREKq2NGzeSm5vLwIEDPbYPHDjQo3tNeXIOsAoQEBBAv379+OmnnwDb/eXgwYMMGjTIY5/BgweTkpLC9u3bAdiwYQP9+/f3mBZ5wIABVK9e3XVdxWn9sn37dp588kmCgoJo3769a7/itJhxqlWrlmuQWadhw4b5LOt+7c6YDx06RGxsbLHPV1mpe46cHXKwUxOfj211EgWc/UlPEREREZGz0q5du1i0aBFvvvkmderUYf/+/YwYMYL27dvz4IMP+iWm4cOHc+rUKaKiohg+fDht2rRhyJAhgG3JER4ezuzZs0lISCAyMpIePXrw4IMP8uyzz7qSExMnTmTLli188sknvPXWW4SEhDB58mRWrlzJ+vXrAVwDwd5///0sXryY9PR0oqKiWLt2LREREURFRWGMYcSIEZw4ccKVuNm1axdNmjQhLCyMqKgojh075jGQrLfIyEgeffRRNmzYwP79+xk2bBht2rTxWbZjx47MmjWLZcuW0b17d+69915Gjhx51g8CC0qayNnmOLZWXwE0AX4FTha6h4iIiIiIVEAjRoxg8uTJjB07lnr16rF9+3Zuvvlmj+mGy9Mdd9zBa6+9xsSJE/njjz+4/fbb2bp1q+v1t99+m5o1azJy5EhGjhxJbGwsjz/+OK+//rqrzK+//kqfPn146aWX+Pjjjzl+/DiLFi3iqaeecpX5/fffefzxx3n00Ud55JFHiI2NpXXr1vz444/cfffdtGrVipycHLZs2UKfPn04ePAgAB999BE9e/ZkypQpNGrUiAULFnDPPfcUeD3jx4/nggsuYOLEiYAd3PXRRx/l888/z1f2qaee4uabb2bZsmVkZmYyYcIE3nzzzdO+p5VBQFXIDPmyadMmExoa6u8wSiw4JBiuhqTfk/wdSsVXFzvLzjZsKxSpVIKDgwFISlJdl7Of6rtUJarvUpWURX1v3749u3btOmPHEylMy5YtiYmJ4eabb2bFihUFlgsKCgIgJyenvEIrscI+O8aYzcDVvl7zx5gmNwK7gX3A0z5e7w78DGQD7h3YemInAXcumcCtjtcWANFur/lrknKpSFKAVOw4J5cB5/g3HBEREREREalcyrt7ThAwA+gNxAIbgU+xnSicfgfuBp7w2ncNecmQ+tiky1durz8JLD3jEUvllgXEAY2AC7CtTo75NSIRERERERGpJMo7adIJm+z4zbG+GOiHZ9IkxvFvbiHHGQh8CaSf4fjkbJWEbWkSChwA9mITKiIiIiIiIuLTgQMHCAgI8HcYflXeSZNmwB9u67HANaU4zh3Aq17bXgTGAqux3X4KHf4zKCjI1cewMqlXt56dUvc8f0dSSaUBbYHWwE5sMkUqpHr16vk7BJFyo/ouVYnqu1QlZVHfAwMDXeNHiFQUlaFOBgYGlioH4I8xTU5XU+wIFavctj0DtMe2I6gPjClg3/uATcCmhg0blmWMUpElYVuZXAlchO00JiIiIiIiIuKlvFuaHASau62HOLaVxGAgAs/OFYcd/54E5pN/PBSnOY6FuLg4UxlHbT854iTVE6qTciLF36FUbiewY5s0wLbc2YYdOFYqnMr4ORUpLdV3qUpU36UqOZP1vXHjxhV6hhKp2ipy3czNzS3VZ7G8W5psJK9zxDnYbjaflvAYQ4BFXtuaOv4NwM6oE3UaMVZcjSF9bDopb6TAAOzVyulJwI6e0wVoQ+VseyUiIiIiIiJlorwfEbOBh7Fda3YCHwE7gPHALY4yodixTgYBsx2vO7XCtlT5zuu47wPbHUtDYGKZRO9vcXD+386n2r5q8Bz27rTwd1BngQzgKDaV1xmo499wREREREREpGIo7+45AF84Fndj3X7eiO2240sMdjBZb71OP6zKIehAEOeFn0fyFckwGjv/0BzgPWxKSkrHYFud1Aa6Aruws+wYfwYlIiIiIiIi/qTOCJVQAAHwGXbi5bXAI8C72KFw5fSkYcc6uRg7QXZt/4YjIiIiIiIi/qOkSWWWgJ0n6AnsgKbvAo8CNf0Z1FkgF9tdpwbQDdshTOPHiIiIiIiIVDlKmpwN1mBbnXwGhGG77Fzt14jODieARKAjcBV2lh0RERERERGpMpQ0OVucwA5/e79jfTZ2sNjz/BbR2SEHiMfex78AF/o3HBERERGRs0VwcDCzZs3i6NGjJCQkMGnSJADWrl3Lww8/7OfoRCx/DAQrZWkTdiLn+4A7sQ/6k4Bv/RjT2eA49tNyOdAYO/dTpl8jEhERERGptOrWrcsPP/zAiRMn+Oc//8mll17KSy+9RExMDBdddBFz5871d4gigFqanJ0ygf8Ad2G7l0wDJmPHPZHSy8a2OgnGjnXSyL/hiIiIiIhUVs899xxNmjThxhtv5LPPPuPll1/m6NGjvPzyy7zyyiucPHnS3yGKAGppcnbbhU2c/AMYAYQCr2HHPpHSSwaqA38GDmHv8ym/RiQiIiIiVdwaP523Zyn3CwsLY+7cuSQkJLi2paSkULduXWbNmnVmghM5A9TS5GyXDcwHhgD7gXBgBtDMjzGdDbKwrU4aYludNPRvOCIiIiIilcXFF19Mo0aNiIyM9NgeFBTEG2+8QXp6up8iE8lPLU2qigPYcU4GYKcl/giYCSzCTrErpZMMnIOdreh3YC82oSIiIiIiUo5K2+LDH1q3bg3AgQMHXNu6dOlC69at2bp1q7/CEvFJLU2qEgMsAwYBG4DR2FYobfwZ1FngFLbVyYVAV6C+f8MREREREanIcnJyAKhfP+8P5ylTpgAQEBDgl5hECqKkSVUUj02YPI190H8feBA7ToeUXiI2gdIJaI/acYmIiIiI+LB582YyMjKYMmUKf/vb35g3bx7169dnz5493HHHHbRs2dLfIYq4KGlSlUUCA4GVwHBsV50r/BpR5ZeJTUo1B7oA9fwbjoiIiIhIRZOYmEhYWBghISF8+umnXH755fTt25cXX3yRfv36MXjw5dLhbAAAIABJREFUYH+HKOKi78KruhRgHDZx8izwNrAEeBPQ+EullwDUBDoD+4Df0NgxIiIiIiIOS5YsYcmSJR7bYmJiWLhwoZ8iEvFNLU3E+hEYDCzGjnmyBDs+h5ReJnAU+BM2eVLHv+GIiIiIiIhIyShpInkygGnAPcAJ4D/ARNTF5HQY4Bj2k9YVaI0+dSIiIiIiIpWEHt8kvyhgGDALuB47404fv0ZU+aVjkycXYweKre3fcERERERERKRoSpqIb9nAXGAo8Du2xckbQBN/BlXJ5WIHiT0H6IYdLFYzqomIiIiIiFRYSppI4X4D7gWmAn8GPsKOfaKH/dI7gZ2euCNwNXCuf8MRERERERER35Q0kaLlYgeIHQz8AozBzrLTyo8xVXY52FYn52JbnVzo33BEREREREQkPyVNpPgOA48AL2ATJouA4Wji6tORCiQDl2Nb8tT0bzgiIiIiUrFlZWVRq1Ytf4chUqnUqlWLrKysUu2rpImU3BfAQOAb4EHgPWxXEymdbGyrk3rYVieN/RuOiIiIiFRc8fHxNGvWTIkTkWKqVasWzZo1Iz4+vlT7q42AlE4S8BywEngGmI9tefIWkOnHuCqzZOwn8v+wrXp2Aqf8GpGIiIiIVDCpqakAXHjhhVSvXt3P0YhYgYG2PUZubq6fI8kvKyuLuLg412enpJQ0kdOzFvgZ223nTuA64EXgJz/GVJk5W500wLY62Q4c9WtEIiIiIlLBpKamlvoBUKQsBAcHA5CUlOTnSM48dc+R05cGTMLOspONbW0yDjjfn0FVcslAOnZ2nY6AvkQQEREREREpd0qayJmzFRgCvAPcBCwBrvdrRJXbKSAOaAJ0Ber7NxwREREREZGqRkkTObNOATOBf2C7lUwGpgEN/RlUJZcEnASuAdqjTnUiIiIiIiLlREkTKRt7gDDgdaAzsAzoDwT4M6hK7CS21Ulz4FrsTDsiIiIiIiJSppQ0kbKTA/wXuB07E8zzwCzsg7+UTgJ23JjOQBsgyL/hiIiIiIiInM2UNJGyFws8AIwHLgYWY1uh6IG/dDKxXZ/+hE2eaMBdERERERGRMqGkiZSf5cBA4HvgUWAhNokiJWeAY9juTtcCrdGnWURERERE5P/Zu+/wyM7y7uPf0Yy0va/XbVl3Y9MDGEIxgRASJySYgCnGgOkl4EASahJ6CJBCSOimGAzGxNgQHF4IIQGCqbbBNhhs3HFbr7dod9Wnvn/cZ3ZGsyNpJI10NDPfz3XNJc1Imn0sj6Rzfue+76fNPM3S4toFvAF4PTEc9nzgHGBZmovqYKPE9/REYlDs6nSXI0mSJEndxNBE6fg2UXXyNeAFwIXAQ9NcUAcrE+06/cTWxNtw4K4kSZIktYGhidIzBLyLmHeSBT4BvBmrJeZqGNgDnAw8HFiZ7nIkSZIkqdMZmih9VxA77JxPbEv8JeB3Ul1R5yoRVScrgccCR6S7HEmSJEnqZIYmWhrGgX8ldtXZC7wfeC+wMc1FdbAh4vv4IOBhwPJ0lyNJkiRJncjQREvLdcDzgA8R1SYXA3+S6oo6VxG4l9iS+LHAoekuR5IkSZI6jaGJlp4icB5wJnAL8Hbgw9hqMlf7gP3EoN0H405FkiRJktQiQxMtXbcBLyXadB4IXAQ8B1+1c1EEdgCbiKqTQ9JdjiRJkiR1Ak8/tbRViMGwzwCuBP4K+DRwXJqL6mB7gRFid50HENsUS5IkSZKaMjRRZ9gBvBb4a2ArcAHwcjzpn4s88f08DHgMDtuVJEmSpCkYmqizfBM4A/hv4GXAF4gdYjR7e4AJ4JHAyUAu3eVIkiRJ0lJjaKLOsxd4K/BqYAXwKeD1wMo0F9WhJoiqk61E1cn6dJcjSZIkSUuJoYk614+AZxIDYqtvH53qijrXbqAA/DZwApBNdzmSJEmStBQYmqizjQL/CLwIGAM+CLwTKybmYhzYCRwDPApYm+5yJEmSJClthibqDr8gtiM+F/h94GLgD1JdUWeqALuS9x9NBCj+lpAkSZLUozwdUvcoAB8HzgLuAv4e+ABwaJqL6lCjRHhyIjEodnW6y5EkSZKkNBiaqPvcDLwQ+Cfg4cSsk2cAmTQX1YHKRLtOP/BYYBt+DyVJkiT1FEMTdacycCExIPZa4E3AJ4GjU1xTpxomBsXejwih3KVIkiRJUo8wNFF3uxt4FfA2Yj7HhcTQ2Fyai+pAJeBeIjB5LHBkusuRJEmSpMVgaKLe8DXgDOC7RIjyOeDkNBfUoYaAvcADgYcBy9NdjiRJkiQtJEOTTlMm5kp4sjp7e4A3A39BbEn8WeC1+L2crSJRdbKWqDo5LN3lSJIkSdJCSSM0OQ34NXATMWmi0eOAnxGnZmc0fKwEXJ3cLq17/BjgJ8lz/jsw0N4lLyFjxH99H3AIkE13OR3pe8Rg2K8AzyNeMaekuqLOtA/YD/wW8GBgWbrLkSRJkqR2W+zQJAt8GPhDYqzkmcnbercDLwC+0OTrx4CHJLen1D3+PuBfgOOBQeDF7Vz0krMX+CHwK6JiYl26y+lIw8B7gJcSUdzHgLcAa9JcVAcqAjuAjUTVySHpLkeSJEmS2mmxx2E+gqgGuSW5/0XgdOL0v+q25G25xefMAL8LPCe5/1ng7cBHp/uibDbLhg0bWvwnlo7169fX7gwTO8McS9TaDAHjqSyrc90AlZdUGD97nPFnj5M5NcPKD6xk4HvdW6y0IEpEBHsqsJ3Y9rkwv6ec9FqXupyvd/USX+/qJb7e1Su6+bW+2JUmRwJ31N2/k9ntw7EcuBL4MfDU5LFNRO1FsYXnfFny9Vdu3rx5Fv/sEjZORE5XEf83N2HLzixl8hlWfGIFa16xhr5dfYy8a4Thdw1T3tRqbicgQpJdwBYiHt2Y7nIkSZIkab46bePVo4C7iNqKbwO/ICYrtOrc5MaOHTsqg4ODbV/gYjlo7YNEjc5W4CSi/mbvYq+qw11FzDg5CwovL7Dvs/vgA8B/pLyuTjNMzDc5AfgNcCO1SHMOOvnnVJotX+/qJb7e1Ut8vatXdONrfbErTe4C7lN3f2vy2Gy+HqK957vECMrdxGSPagA02+fsHmViIsxlxHdlC+4MM1sl4Hzg2cS44rcQ8062prmoDjRB7LCzFXgM0HmdcJIkSZK06KHJFcT152OIHW6ezeRdcKazgdr+HJuJU7FfARXgO9R22jkb+Gqb1tuZxoBrgMuJVp3NuLn0bN0BvAL4O+BkYoed52Hr02ztJtp2HgmciN8/SZIkSR1lsU+li8CrgW8C1wEXAb8E3kltN5xTiLkkzwA+nnwc4tT1SiIO+A7wXmoDZN8I/CUxZHYT8KkF/u/oDHuIXXZuIOZLuMvO7FSIbYmfDvwIeC3wGeLkX60bB3YSzXWPAtamuxxJkiRJalUaM02+ntzqvbXu/Sto3gzxQ+CBUzznLcToSTUqEbNOdgD3BQ4npsC4y07rdgGvA55IxHOfI1p4PgHkU1xXJ6kQVScrgUcTc05upfU9siRJkiQpBTZt9Iox4GqiZacfW3bm4n+JJrCvAy8CLiSm6qh1o0QIdRzw28DqdJcjSZIkSdPxtLnX7Aa+T1zpt2Vn9vYD7wBeSdRpfRJ4M7AqzUV1mDIRnGSBxwLbiN2eJEmSJGmJMTTpRSWiNeL7xLbEW6iN2FVrLgeeBXwe+FPgS8Cpqa6o84wQ4cn9iOa6lekuR5IkSZIaGZr0slHgKmK87jJs2ZmtceBfgBcSFSgfAP4et9edjTKxNfFyourkyHSXI0mSJEn1PEVWXO2/jGjZ2YS7m8zWL4HnAh8BngBcDDw51RV1niGi6umBwMOAFekuR5IkSZLA0ERV1Zady4iqCVt2ZqdIbHR9JrFb0TuBDxK7Fak1RaLqZC1RdXJousuRJEmSJEMTTTYK/Ixay84mfJXMxm3AS4D3AQ8GLiKCFL+HrduX3O4HPIBo3ZEkSZKkFHgqp+Z2EYNibyFmnaxJdzkdpUKEJc8kAqjXAZ8Gjk1zUR2mSLwG1wGPA44mdtuRJEmSpEVkaKKpFYGbiZadYaJlZyDVFXWWe4DXAH8L3Af4AvAyoD/NRXWY/cAgcCKxO9Eh6S5HkiRJUm8xNNHMRoCfJrflRMtOJtUVdZZvAE8HvgW8HLiAaDtRa0pE1ck4MST2ETisWJIkSdKiMDRR63YSLTu3Elf8bdlp3V7gLcCfA6uA84i2HXeJaV2e2vbEjyZmnjisWJIkSdICMjTR7BSBm4jwxJad2fsB8AzgS8CziNknj0p1RZ1nmAhPDiPmnRyF804kSZIkLQhDE83NMNGu8zOiWsKWndaNAv9A7LIzAXwIeAcx9FSt25vc7ovzTiRJkiQtCEMTzc+9xKDY24iT1tWprqazXAM8B/gkcBpwMfD7qa6o81TnnUwQ805OwXknkiRJktrG0ETzVwRuJFp2xoiWHXeIaU0e+ChwFnA38B7gX4jvoVo3QQR4K3DeiSRJkqS2MTRR+wwDVwBXASuxZWc2bgJeCLyf2B3mS8AZ+P2brcZ5J9tw3okkSZKkOTM0UfvtIKpOfoMtO7NRJrYjfiZwLfBm4Fxi0Klmpzrv5CScdyJJkiRpzgxNtDAKwA3EbjHj2LIzG3cBrwLeDhwPXEhUoeRSXFMnct6JJEmSpHkyNNHCGgIuJ1p2VgEbseWkVf9JtOhcBrwaOB84OdUVdabGeScn47wTSZIkSS0xNNHi2EGc/N+JLTuzsRt4I/BXROD0WeA1wPI0F9WhqvNOjsB5J5IkSZJaYmiixVMArgd+SFz934ItJ636LlF18lXg+cAXiXYTzd4gzjuRJEmS1BJDEy2+/UTLzjXAGqKCQjMbBt4NvByoAB8D3oJVO3PRbN7JmlRXJEmSJGkJMjRROirAdmotO1uImSea2ZXAs4HPAH8MXAI8Ic0FdbD6eSePwXknkiRJkiYxNFG68tRadgrYstOqCeCDwNlExcQ/Ae8DNqW5qA7mvBNJkiRJTRiaaGnYD/wE+DmxLawtO625nghOPkjM57gYeEqqK+ps9fNOHovzTiRJkqQeZ2iipaMC3A18D7iLqDpZmeqKOkORaNV5NnAj8Dbgo8DWFNfUyarzTvI470SSJEnqcYYmWnrywHXAj4AycbXflp2Z3U4MiX03cD/g34HnYZvJXDnvRJIkSep5hiZauvYRwckviJadDekupyNUgC8T2xP/GHgtcB5wQpqL6nDN5p34m1OSJEnqCR76a2mrtuxcRuy2Y8tOa3YCfwW8CTgM+DzwZ8BAmovqcPXzTk4FNqe7HEmSJEkLz9BEnWEC+BVRPVHGXXZa9S3gGcA3gBcDFwIPSXVFna1+3snDcd6JJEmS1OUMTdRZ9jK5ZWd9usvpCPuAtwOvAvqBTwFvBFaluKZO57wTSZIkqScYmqjzVIjddS4jTly3ECevmt6PgWcBFxAzTy4ittXV3NXPOzkV551IkiRJXcbDe3WuCeBaIgwAd9lpxRjwfuCFxAn/vxK77Thkd34GiYoe551IkiRJXcXQRJ2v2rLzK2Adtuy04lrgLOBjwBOBi4E/SnVFna9x3snDcN6JJEmS1OEMTdQdysAdTG7ZWZ7qipa+IvAJ4DnA7cC7gH8jdtvR3FXnnazCeSeSJElShzM0UXcZJ6oofkK8ujcD2VRXtPTdQuys84/AbwFfImaf+NthfhrnndwHv6eSJElSh/EQXt1pEPghcB3RrrMu3eUseWXgi8T2xFcDbwA+CRyT5qK6xCCwH7gfMXjXeSeSJElSxzA0Ufeqb9nZDRyKLTszuQc4B/hb4CjgC8BLccDufBWBnUAB551IkiRJHcTQRN1vHPg50bKTJXbZsWVnet8gtiX+NvAKYpviB6S6ou7QbN7JQKorkiRJkjQNQxP1jj3AD4iWnQ24y85MBoG/AV4LrAbOA/4Sq3XaoX7eyeNw3okkSZK0RHmYrt5SJnaKqbbsuMvOzC4DnglcQmxTfBHw26muqHs470SSJEla0gxN1JvGgGuAy4lWHXfZmd4I8F5il50C8GHg7cDaFNfULarzTorU5p2sTnVFkiRJkhKGJupt1ZadG7BlpxVXA2cCnwL+ELgYeFKqK+oe49TmnTwWOAnnnUiSJEkpMzSRysBtRBvKHtxlZyZ54CPAc4EdRAXKPxMDdjV/w0TlyVacdyJJkiSlzENxqWqMqKS4HOgnWnb8CZnajcALgA8QM04uBp4GZFJcU7eoEAFedd7JY3DeiSRJkpQCTwmlRruB7xOhwEZgXbrLWdJKwOeAZwG/Inbb+TiwLc1FdZHqvJMScArOO5EkSZIWmaGJ1EwJuJUIT/YSu+wsS3VFS9udwCuBdwInAl8kqlByKa6pm4wTrVCrcd6JJEmStIgMTaTpjAJXAVcSoYktO9P7KnAGETadA3yWOMFXewzhvBNJkiRpEXm4LbViFzEo9kZgE261O51dwBuA1xEh02eJAMVKnfaon3dyMjHvZFOqK5IkSZK6lqGJ1Kpqy85lxAmrLTvT+w5RdfI1olXni8RMDrVHkQioSsAjcN6JJEmStADSCE1OA34N3AS8qcnHHwf8jDglOKPu8YcAPwJ+CfycGD1Z9RnidPbq5PaQdi9aOmCUeIVWW3Y2Yfw4lSHgXcAriO/RucSwWE/u28d5J5IkSdKCWexTvSzwYeAPiY00z0ze1ruduC79hYbHR4HnA/cngpcPAOvrPv56Iix5CBGcSAur2rJzC9GGsibd5SxpVxAx5/nA6cT2xI9Pc0FdyHknkiRJUtst9iH1I4gKk1uAPFGwf3rD59xGVJKUGx6/gZgoAXA3cC9wyEItVGpJCbiZCE+GiZYdr/I3Nw78K3A2MAj8M/A+nMfRTs47kSRJktpqsTcEPRK4o+7+ncAj5/A8jyBOTW+ue+zdwFuB/yXafiame4JsNsuGDRvm8E+na/369TN/ktJxC7APuC/xk7WXOInVZHdA5RUVxs8cZ/z542QekWHFR1Yw8I0BMmQOfNr6Vb7W52UcWAH8DrCb+G05kuqKNA1/t6uX+HpXL/H1rl7Rza/1TizePhz4HPBCatUobyY6+U8BNgJvnOJrX0ZMorhy8+bNC7xM9aTdwOVENLgJZ3dMIVPKsOLzK1j74rVkb8sy+qZRhv95mNLhpbSX1l3GiTayVUTUfDxWQkmSJEmzsNiVJncRnfZVW5PHWrUW+H/EKMkf1z2+PXk7AZxHbHbazLnJjR07dlQGBwdn8U8vLZ289p6wkxh3fBLRRLaXaEjTZNcBLwKeDsVziuw/bz98FLiw9imDw77W520YyAAbgAcC1xNNjo1NkEqdv9vVS3y9q5f4elev6MbX+mJXmlwBnAAcQ1zvfDZwaYtfOwB8hRgleXHDxw5P3maApwLXznul0nyNAD8ldtpZQVSeZKb9it5UIX6in0n8hvhL4DwoHWvVSVvVzzu5P847kSRJklqw2KFJEXg18E3iGvNFxBbC7wSeknzOKcSsk2cAH08+DnFK9ThiZ53GrYUvAH6R3DYDf7ew/xnSLNxLDIq9jag6sWWnuR3AXxDNdkfA/k/sZ+xFY7A85XV1myJRCVUifts+FF+TkiRJ0hQWuz0H4OvJrd5b696/gmjbafT55NbM77ZhXdLCKRJ7P20ndjXZQuwgU0hzUUvUfwOXw8AbBhg/exyeDHySqDMrpru0rjKe3NYAjyVCveq+ZpIkSZKAzhwEK3WuYSIWvApYiS07U9kLq/5+FWtetQZuJ/bDugQ4Db9f7TZEVJ5sJWr5jsS/DJIkSVLCQ2MpDTuA7wO/wZadaeSuzcFLgXOIGTHvJprxHpPqsrpP/byTB+C8E0mSJClhaCKlpQDcAPyAaJPYAvSnuqKl64fAWcBfE9vn/hvwCeDBaS6qCzWbd7Iq1RVJkiRJqTI0kdI2BFxOtOysAjZiC0ozFWKE9NOB9wDbgE8D7weOT3Fd3WicGGC8BjgVOJHYv0ySJEnqMYYm0lKxg9hl505s2ZlOkdii+HTgQ0Q1xIXEHlxHpLiublSdd7IN551IkiSpJ3n4Ky0lBeB6oh1lgmjZSWOPq04wDpxHbFZ+PvBE4MvA64lqHbVH47yTR+O8E0mSJPUMQxNpKdpPtOxcQ7RIGAJMbT/wQeCpwFeBM5K3r8RqnXaqzjsp47wTSZIk9Yx2hiYZ4FltfD6pt1WA7dRadrbgSep0dhKzTp5BfM9eQoQnzwWWpbiubuO8E0mSJPWQ2YYmh3DwiMoVwKuBm4AvtGNRkurkqbXsFLBlZya3E7vsnAX8CvgLom3ndCCb4rq6jfNOJEmS1ANaOcRdCZwLjAD3AIPA65KPvRy4jdgA9Cbg8W1foaSwH/gJ8HNgLbbszOR64Bzit9RO4K3ARcDvprmoLtNs3omvS0mSJHWRVq5XvxU4m9jc8xrgKOI67iOJzT+/DbwZuGKB1iipqgLcDewCjiN+GoeB0TQXtcRdCbyAiHRfBfwj8EtiDoq/tdqjOu9kOfAIon3n10TULkmSJHWwVkKTpxGbeb677rH/A75OBCkvWYB1SZpOHriOCFDuTzTODRInr2ruu8D3gCcT1ScfIyp3PkS08Wj+xpPbWmLeyS3ArURbmSRJktSBWmnPOYoISepV73+2vcuRNCv7gB8BvyBOVDeku5wlrwz8J/CnwD8RQ0w/B7wPODq9ZXWd/Rw876RxGpYkSZLUAVoJTfqJ69r1qvctvpbSVm3ZuYzYbedQYhKRplYALgSeQlScPIqYd/IW4vun+avOOxki5p08BuedSJIkqeO0ugfHOcTpWFX1muFrgB11j1eAN7ZhXZJma4JoM7mLaNnZQpy02rIztVHgE8CXgBcR2xX/IRGgnEdU8mh+6uedPJL4i+G8E0mSJHWIVkKT24HHNnn8N0ThdT1DEylt1ZadI4CTiZaUvamuaOnbC7yf2DT95cBziBaezwEXAGPpLa1rOO9EkiRJHaiV0OTohV6EpDarEBUnu4ATgK1Em4Qn/9O7B3gHEZb8GfBK4JnAp4Av4wl+O+wnXovbgPsQA423E69ZSZIkaYlpZaZJvU04zk/qHBPAtcCPiZPSQ2i9Ka+X3QK8jths/VbgDcAlwB8x+9+aOlj9vJMH4bwTSZIkLVmtDoL9B+L64L3EFIB/J06/JHWCvURw8itgHbA+3eV0jGuJdp1XESf47yIGyJ6a5qK6SJH4q1IGHgE8FFiV6ookSZKkSVoJTd4I/AURlLwK+DfgD4jxiZI6RRm4A/gecaK6hRjOqZn9GHgu8CYiRv4A0bLzW2kuqouME6/JtcQErROJ77MkSZKUslYK9c8irq++s+6xy4CvEtcE3QNB6iTVlp3qLjubgUGglOaiOkAF+BbwHeBPgJcBnwS+D3wYuCG9pXWN/UQDqPNOJEmStES0UmlyLHGaUO9/iUPbo9u9IEmLZBD4IXFiup5o29HMisBXgKcSFScPJFp23k0M3NX8OO9EkiRJS0irM00mGh7LJ2+XtXc5khZVtWXnMmA3cCi27LRqgthl5ylEq87jiWGxbyKqdzQ/jfNOHoLzTiRJkrToWt1H4xyiSLqquoPOa4AddY9XiBkokjrJOPBzIkB5ADHmeQ+27LRiGPgIcBHwYuBpRPvOF4DPJh/X3I0nt/XEvJNbgNtw+2dJkiQtilZCk9uJQ9VGvwEe1/CYoYnUyQaBHxBtJicRV/v3prqizrELeB9wAfAK4EXA04HPEIHKeGor6w7VeSdHEzNPnHciSZKkRdBKaHL0Qi9C0hJSJqLSncAJwBHECasn/a25E/hb4Hxiv7HXAGcC5wL/SQRRmpsK0UaWI2bJHEOEJ3vSXJQkSZK6WSszTf4buG/DY7+L3eVSdxsjWnYuB7LEnI5sqivqLDcQgclLgLuJIOVLwJOoNThqbopEqFehNu9kZaorkiRJUpdqJTT5PSbvq5ElNt5sDFIkdaM9RMvODcAGYraEWncVMevktcQI7fcCnwceleaiusQ4MSx2PXAqURnVn+qKJEmS1GVaCU2a8Tqp1EvKxPDNy4gQxV12Zu8yok3nb4E1wIeAjxODdzU/+4mZMkcTk7aOwL9SkiRJaou5hiaSetEYcDXRstNPtOz4W6R1ZeAbxA477yNmcnwW+Cfg2BTX1Q2q806GiHknjyIqoyRJkqR5aPV0p9n+BO5ZIPWq3cD3iZadjUxu4NPMisSOOqcT2xWfAnwReBtwWIrr6gbVeScZ4JE470SSJEnz0sruOQDf5OA9H/63yWMAW+a1IkmdoUS07NxLTDg6FNgHTKS4pk4zBnwKuAR4AfBM4DRiYOyncbvn+RhLbhuIlp2biddrIcU1SZIkqeO0Epq8Y8FXIalzjRLDTjcT8znWEHNPymkuqsPsBT4AXAi8FHg28FRiYOwFwEh6S+t4+4iqk6OB+wDXA9uxVlKSJEktMTSR1B67iGGn24ATiYqT/amuqPPsAP6OCEteCbycqD6pVqPk01taR6vOO8kR806OBq4DBlNckyRJkjqCIxwltU8JuJUIT/YTzXrLUl1RZ7oNeCPwPODXwOuALwN/gr+156N+3slv47wTSZIkzcjDb0ntNwr8DLiSCE024W+bufgV8Cqi6mQP8HZiYOzj01tSVxgjqnqq806OJ3aDkiRJkhp4GiNp4VRbdm4hZp6sSXc5Hety4PnA64Es8M/AZ4CHp7imbrCPqDw5BjgVOJyoQpEkSZIShiaSFlaJ2LnkMmCYaNkZSHVFnevbxIyTdwCHAB8HPgSclOaiOlx13skw8GDgUUQFiiRJkoShiaTFMgL8NLktJ1p2vKo/eyXgUuBPgfcDJxM77LyHGMKruSkS22dngEfivBNJkiQBhiaSFttO4PvEwNhDsGVnrvJEWHI68AngscCXgL8mvq+amzEiPNlAtOw470SSJKmnGZpIWnxF4CZs2WmHYeBjRHhyMfAU4D+Ac4C1Ka6r0+0jZvI470SSJKmnGZrCoMZsAAAgAElEQVRISk+1ZednwAps2ZmPPcA/Ak8D/ocYHHsp8EKiHUqz57wTSZKknmdoIil99xJVJ7cRrSWrU11NZ7sbeBtwJhFIvRr4KvAMIJfiujpZ47yTB+O8E0mSpB5haCJpaSgCNxLzTsaILYqdJTF3NwF/RVSa3A68CbgEOA2reeaqOu9kI9GycxwGUZIkSV3O0ETS0jIMXAH8glrLjiemc/dz4KXEjJMR4N3EANnHpLmoDrePaNs5FngczjuRJEnqYoYmkpamXcBPgF8TA003Y3gyHz8EziJ211kF/Bux686D01xUByvjvBNJkqQeYGgiaekqEq0l3wWuI2adHIJtO3NVAb4JPB14D7AN+DTwfmJrXc1e47yTB+G8E0mSpC5iaCJp6SsCdwD/R61t5xDcpniuisT2xKcDHwIeClwIvBM4IsV1dbLqvJNNOO9EkiSpixiaSOocJWJ3mO8B1wDLgC3JW83eOHAe8BTgfOCJwJeB1xPDTjV7zjuRJEnqKoYmkjpPGbiHCE9+RlzR3wIsT3NRHWw/8EHgqcT2xGckb1+J2z/PRXXeyQi1eSfrU12RJEmS5iiN0OQ0YrTjTcQmmI0eR5wGFYlD93pnE5uS3pi8X/Uwomj/JmK8odf1pF5QIVoivg/8NHlsC9G+o9nbScw6OQO4DHgJEZ48F6t55qJAbd7JbxPzTnxtSpIkdZTFDk2ywIeBPwTuB5yZvK13O/AC4AsNj28E3kaM2ntE8n51r4KPEptqnpDcTmv/0iUtWRXihP+HxHbFZSI8cSDn3NxB7LJzFvAr4C+Itp3Tid/imp3qvJPNxGUB551IkiR1jMUOTR5BVIPcAuSBLxKH4fVuA35OnPbU+wPgW8AeYDB5/zSiY3wt8GPi1Ol8oshcUi/aDfwIuJz4LbMFW0zm6nrgHOBlxEn/W4GLiNknmr291OadnIrzTiRJkjrAYl/rOpK4hll1J1E5MtevPTK53dnk8Wlls1k2bNgw06ctOevX2xiv3jDv13qFaORbBxyd3MaIOROanV9D5ZwKhccUGHvpGOV/KJO9PsuKc1fQ/1P3f561CWLb7EcBw8ANsD7j73b1Do9l1Et8vatXdPNrvdcGwb4MuBK4cvPmzWmvRdJi2EfstPNTIjDZDKxJdUUdKUOGgR8MsPZFa1n59yuprK8w/P5hhv55iOJJxbSX13kKwC6i0uShRGOpg4wlSZKWnMWuNLkLuE/d/a3JY61+7eMbvva7yeNbW3zOc5MbO3bsqAwODrb4Ty89nbx2aTba9lofBH5DNPMdCxxGXPHf156n7ymXAJcCZ0DxxUWGPj4E/0NMl7ot1ZV1nmFiHs+RwEkweJ/BCFQKxDj0PLX7heR+kdh+u/FWbnhfWuI8llEv8fWuXtGNr/XFDk2uIK6nHUMEG88GntPi134T+Htqw19/H3gzMeNkP7E3wU+A5xObZ0rSwfYDVxNzTo4hTlbzxLwJta4AXEjsrnMW8DzgCcB/EtH0jvSW1pGq4d0wUQPaRwzdXQGsqrtf/dhUKtTmpBQ5OGypf1tg6tDF8EWSJAlY/NCkCLyaCECywKeBXwLvJNpmLgVOAb5ChCN/ArwDuD8RjryLCF5IvmZP8v6fAZ8hDi+/kdwkaWrDxEbltwDbgKOIE8l9xImnWjMKfAL4EvBC4JnE/mhfAs7DMGouysltvl1PfXW35dRCl+nCl/rQpaoavjQLXerDl6lCl+r7kiRJHSiNTQ+/ntzqvbXu/SuY3G5T79PJrdGVwAPmvzRJPWcEuI5oKzmKCFDKxMm+V9lbtxf4F6L65GXEhvJPBT4HXEAM4dXiqoYv85WhFrQsI7byrg9k6rehbha6VJU4uO1ousqXqSpgJEmSFlEaoYkkLT1jxBa7txGTl44hTgAHMTyZjXuIOsDPETWArySqTz4FfJk4MVZnqTD/qheYHL4MENUv9ZUv2am/dFIYU2b6tqM8rbUdWVEmSZJaYGgiSfXGia2Kbydq3o4hTtb24lXu2bgVeD1RA3gO8AZi9snHgP/CIKoXtTt8ydA8fOnj4GqXZhUw9eFLswqY6mMztR0ZvkiS1NUMTSSpmQngZuAOYljs8cnj+2jPiV+vuBZ4OTGq+9XEZKqzgQ8D30txXepc9eHLfCuXqkFLP9F6tIbJbUfVoGWqtqNqYFKg+S5H9eHLTNUvhi+SJC1JhiaSNJ08UTVxJ3A4sf9Xlqg8MTxp3Y+J/c1+j2jZ+RfgGmKvs6tSXJd6WzWwaFf4kiMCmMbwBaYOXeqDmWbbTNe3HdWHL1NVwFjFJbVPpu5tpsn9Vj62GltTpQ5naCJJrSgQLTt3UwtP+onwxIOh1lSAbwHfIfZGexnwSeD7ROXJDektTZqXdoYv1fajfia3HFXbjurDl6kqYBorX+orYKrvz9R2ZPjSG1oJA1r9vHY8R98M7/c1PM90XzObjzU+XtUYbE416Hq6z1uZ3N8BbCdmpe3HnzGpgxiaSNJsFImWnbuBQ4ETgfVE204+xXV1kiKxsfzXiSGxLyR23fkv4KNEVY/Ui6pzk9q13XQWWEFc6a4fxFs9KZyu7ShDrdKlMXCpv7UydDcti33C38pzNAZgje/3NXzufMOAqZ6v3lyCgek+1vh5s3n+6ttKk8em+lj949N9rDTNxxrfb6fVydsycCxx9lUGdhEhyn5gdAH+XUltY2jScfqJPVGHk/vVWtzqb/rG9+u3CJjqL0OzvzQL/TGpw5WI4OQeYAtwX2rhyUSK6+okE8QuO18Bng88h2jf+QpRgbIrvaVJHa3657+d4ctyYFXd/foT/EaNJ8bV4KV6W548NszcT/5bqRKYak3zOamfz3NMd4I+08fqH5/qY427Qk33dVp81TY7iNfHauCByfsTxPHETiJEsf1XWlIMTTrOAHA08Vu12WWMxvvNLinA3I8K5vIc06kPeZqFPpUmn9cYBs3lY43/1mKFSLP5PHWEMnGgswM4hAhP1hEHPeMprquTDAMfAS4CXgw8jWjf+QLwWWoZsaTF1e7wpY/awN1M8j60ViVQ5uA/kf75VKeqACPJDeKM7EjiEL9CtPBsJ1qA/Rsopc7QpCMVgaG0F9FG04U89fcb95Fs9euafaz+8enqVBvvL8QlqJk+1izgaSVsauVj9Y9NV7GURojUX/dYB6gA9xJ55mZi5skW4kd1LMV1dZJdwPuAC4gdd14APB34DBGoGEJJnalxQG316NOTQSkUiYCkajlwMnHoW2ByFYrVrNKiMzTREuDloelNF/I0NkpD7cd6qobq+Xys0uT+bMOgmZ6j+rGVyf39RBqxi0gglnjjb4U4sNkJbCJmnmwhTg6W+NKXjDuBtwDnA68CXkO07pwLXIply5Kk7jZO7UJBlqhk3UocHg0R7cGDyfsOlJUWnKGJtOQ1q1fuBdXJaWNE+nAkcbSQp1bSscSTiN3Aj4CNwPFEeDKKV1dbdSPwWuAhwDnA3wDPI1p5/ofe+5GQJPWeEhGOVIvMlxHHFH3ULtRUB8pa2SotCEMTSUtciUgZqklDllqIAlG3Wg1RlmgvzB7gcmJQrOHJ7F1NzDo5FXg18F7geuBDRCglSVKvmKDWopMB1hLHFRniEGg7cdHGgbJS2xiaSOowzUKUzcARxBFDgZjKWm3nWUIhyl7gSmJQ7HHEQc44cWCjmV0G/AD4A+CVRGhyJfBB4NoU1yVJUhoqTD4kygH3IbY2rhAXbbYTO/t5oUaaM0MTSR2uWrdaVd/8C0syRNkH/IzYQeJY4HDiqtG+NBfVIcrAN4BvAX8KvJTYYec7RNvOLektTZKkVDUOlF0B3I9o5ckzeaBs/qCvljQFQxNJXaax+bdxglqeJROiDAHXADcT2wxuJZa3d5qvUSgCXwK+BpwJnA18Efg68DHiwFCSpF42Ru0wJwscSlSiwMEDZZ0TJk3J0ERSl2sMUXIcHKLcQzQApxSiDBPtJbcC24CjkmXtw4OYmYwBnwYuIbYofhbRvnNx8vhgaiuTJGnpKDG5HXgZcAIRppSJ60k7cKCs1IShiaQeU+TgEGULtUsvBSJE2UWkGYt45DACXAfcRgQn24gDmb24peBM9gH/SlSbvJQIT04HPg9cQHxvJUlSaBwoux44LHl/lKhC2UOEKKU0FigtHYYmknrcTCHKBLE7T7WdZ3zhlzRG7A5zW7KMYzA8adUO4O+IsOSVwMuBZwKfIqpR7OGWJGmyxoGy/cTFm+M4eKCsFyHUgwxNJGmSZiFKfRPwIoYo48CNwO1EN9ExxBWgvXjVZya3AW8ETia2KX4dcBbwcWLuid8/SZKaKzB5vtpK4P4cPFB2X/K5UpczNJGkaRWZ3ARcDVG2EZdfFiFEmSCGxd5B7Kx8QvL4vmR5mtp1wKuAU4jw5O3A84mddr6T3rIkSeoYo8kN4jDoMOIwCCJc2Z68daCsupShiSTNylQhyn2IMpBxFixEyRMVFHcR2xRXB7jtxfBkJlcQO+w8gQhR/okYvvtB4MoU1yVJUicpEhdtqpYDJxLHIyUmD5RdhI5maTEYmkjSvLQSouygtjtPG44gCkTLzt3UwpN+IjyxTHZ63wG+BzyZmHfyceBHwIeIOTKSJKl149QObfqADcSxCUR1ynZqh0C2xqpDGZpIUls1C1Hq61gniBClWokywZwViZadu4mc5kRi+v0+HHg6nRJwKfBfwDOAFxE77Pw38FEikJIkSbNT5uCBskcDxycf201toOxok6+XlihDE0laUDOFKI3tPHMIUUpEcHIPsfHPfamFJ/PIZLpenghLvgo8lxgU+7vJ/U8QQ+4kSdLcFIDBuvsrgQcShbh54thlF3GYZKWsljBDE0laVM1ClMOZHKLUt/PMIvUoE8HJDuAQovJkC/YVz2QY+BhwEVF1cgbRvvPvwGeY/L9LkiTNTeNA2SOIrY0hLvTcTbQaD+NAWS0phiaSlKrGiWrVo4ijiSOGMaISZRYhSiX5kp3AZmLmyZbky8fate4utIcYEHsB8ArgecDTgM8CF2LwJElSuzQbKHsSMRelSFwAuherZrUkGJpI0pIyVYhyFFHPOkrLIUqFCE52ApuohSfD2Es8ne3A24DzgT8jtip+NvBJ4Cu4U5EkSe3WOFB2E3Bkcn+I+Ns8SFR/lhd9depxhiaStKS1EqJU23mGmTJE2Z3cNhID2bYkXzrc/NMF3Az8FfAg4BzgTcTsk48C38TSYUmSFkKZCEqGkvsDwLHEIVCZmIOynQhQvAikRWBoIkkdpVmIciTRzgPRf1M/E6VhG509wOXEoFjDk9b8HHgp8GjgVcC7gbOJbYp/kOK6JEnqBXlqhzMZYDW1gbITxDy3nUSIYjWoFoChiSR1tMYQpR/YSi1EaWznSY469gJXAuuA44jwZByHnk7nh8CPgCcRbTv/BvyMCE+uSXFdkiT1igowktxg8rWjCtHCs53aQFmpDQxNJKmrFIgjhapqiHJMcn+EqETZAwzBvnyc+K8hSl8PJ67a1OcwqqkA/w18GzgdeBnwaeB7wIeBm9JbmiRJPafI5MOe5cDJxFyUApOrUBwoqzkyNJGkrtYsRLkPkZBAXIa5F4b2wDVDcHM+rtZsJYpS6r9UNUXgEuD/EUNizyZ22PkG8HHgrvSWJklSz6ofKJsFDiGOaTJEwe3dRDXKEA6UVcsMTSSpp8wQogwPw7X3ws17YNsQHJOP8GQfDj5tZhz4DBGgnA2cCfx+cv9TREGPJElafCUmD5RdRsxz66O2w2B1oOxYGgtUpzA0kaSeNkWIMnYM/DoDtw7D1h2wbQ/0DcP+vFdmmhkiZpt8kRgaewbwFOALwOewr1qSpLRNUGvRyQBriZluGSI02U6MgHOgrBoYmkiS6jSEKPkBuGUb3HFslLgeMQLLdsBYMhOlr5DSOpeoXcB7gM8DrwBeQgQonwEuwn5qSZKWggpxQaN6USNHrfC2QlSKbicqbb3w0fMMTSRJ00j2+SsQfcD3DsAh2+DQY+PKzOgw9O2A3CD0GaIccAfwN8D5xDbFryVad84F/pMoGZYkSUtD40DZFcD9iGOdxoGy+YO+Wl3O0ESS1LpiHrbn48DhEGDrAJSOguHjoVSJFp5+Q5QDfg38OfAw4NXAW4DnAR8B/jfFdUmSpKmNUZtzkgUOBbYRVSiNA2Wd+db1DE0kSbNXJMpWd+Zhcz5KWrPAvgHIHwUTx8fnZYcgZ4jCT4EXAr9DVJ78A/BLYg7K5SmuS5IkTa9EVJhULQNOII57ysCO5OZA2a5laCJJmrsitZLVTcC2POTy0f9bBMpNQpT+eyC7tzdDlP8DLgP+iJh58lHgJ1D8dJHc9f5JliRpyWscKLseOCx5f5TJA2Vtx+0KHqFJkuavBNxLDELdCBwFrAGG8tHSU1UegImjoZIDMnUhymC09vRCiFIGvgZ8E3g68GIY+vgQ2V9mo9R3hDjoqr4dbfJY/cdGiStblgdLkrS4GgfK9hNtPM0Gyo6ksUC1g6GJJKl9ykRwshvYABxNhCfDxCC1vnzcDnz+siREqVaiDNdClOwQZLp4z78CsUXxpbD8BcspPrQYgdNWYBWwMnnbijIRnMwUtkwVwIw1fM54G/77JEnqNQ2bELISuD/QRwyQrVbn7ks+Vx3B0ESS1H7Vqyt7iPDkKGA1cWJeP3W+byJuVeVlMHFMXYgyFINluzlEGYUV56+A82FweHDyxzLEBP9qgNLsbf2t8WOHNjy2vMU1FTk4SGklgGl8vPq+B4aSpF5U/VsIceZdHSgLEZzcTYQsDpRd0gxNJEkLazC5rScOFDYQBxATTT53yhDlBKAyeSZKt4Yo9SrUDrh2teH5skQIM5cAZiVRCVP/2ECL/26B2QUwYzN8jj3ikqROU2TyQNnlwInE3+YSkwfKWvG5pBiaSJIWx97kto7YbWcDcXI83YFB0xDl2GQmSgWy+5NKlB4JUearxOTe6/nKMfcAZjWwpeGxVo9Kxpk5gJkpeKl/zKt7kqTFNk7tGKiPOC46PLlfP1B2CC8WpMzQRJK0uPYlt7XUwpNxWtumr6UQ5R7I7jNEWQxFav8/22EZzYOXVU3eb3xsAzEPpv7r+lr8d2dqN5rNfBivDkqSZqvMwQNljwaOTz62m9pA2dEmX68FZWgiSUrHfuCXRMXBVuKkd4LZHQw0DVGOg0qW2J1nX107z7AhylJX3cZxcKZPbEGGKH2eSwCzkqiCqX9sRYv/bompq1xmG8CMMnkGkCSpNxSY/LdwJfAAagNl7ybadvfj3LBFYGgiSUrXMHA9k8OTPHPbmq8+RKkAleV1IQp1lSiGKF2vQoQXrVQwtaKPOGhtNhNmpgBmFTHTp/6xZS3+u0Wm3+lotltU+5JXJ+hLbtnk1tfwdqr3q1+Xa/Ic0328leed43OM9I2Q/XUWfgDcjO2AmpvGgbJHEEP2YfJA2WF8jS0AQxNJ0tJQDU9WAkcCm4mrJ3Odv5EBMuPQl/RLHAhRjodK0reR3dcwE8WmYU2hvnR6ZxueL8fkAGamHZIaH9vc8FirR3TVaq6pdjqaTQAzSnxf1FwrJ9ozBQJzOZlvZ9CQ1nMsdUXitV8mqstKde83PFZYViD/B3n4c+Kk9krgp8nbW1JYuzpftTW2ajlwEvHzUwDupTZQttnQfc1aJ/xaUp1C4QnAccBhxG/lWfzWbvrxxueQFlKGXC5LX1+WbDZLNttHNpujr6+PbDbLsmXL6O/P0d8/wMaNa+jvz7F37yijo6OMjIwwMTFOPl8gn89TLFqL2LVGgRuBO4krKVuYX3hSNW2Iko0HDFG0WIrEcL+hNj1fP3MPYNYSwwfr25iyLf6747Q+cDd5P1/OkylnoqJsLlf0Zxs0pPUcS1318K/+8HAuh5bVt/k2PEc71tHsOab6+FwPnWdh/er1lA4tsf/k/fBw4vZ7yQf3UAtQrgRum91zS8DBA2U3EhefIP7GbCdaffbj6d4cGZp0lAzDw+cv8L/RjuBlLs/Rjr9i7X6O2f639o5Mpu9A4JHNZunr6zsQhuRyOQYGBujv70/e5sjl4v2+vj6mqhmsVKBUKlEulymXS+RyOYrFEplMhnXr1rF58+ZJX1+pwOhoNVAZZnx8gkKhwMTEhIFKtxgjSpnvInLiw4gfv3bt/NJSiLI3CVH2GaJoaStQ26GqHZYztwCmujX11oaP1RmZU+/dFIq07xCl2IbnWKxDpfkGDZbvL6rsjmz8Pfta8sCRwMOohShPSh7fRS1AuRK4Y5EXqs7XOFB2ADiWOOsvE6+x7USA4kDZlhmadJQKa9b8CXB/hoZ2UrucMd9ayIVs9My1uKaZ1tEJL9XOC4gymQqZTIW+vuqNA29zuQzZbIZcLkN/fx+5XPWWSb4m/u1MJm7V9yuVEpVKiXK5CBQpFosUCkWGhwtkMoUDnzf57cHfzf7+eFso5CkU8owdNJcgQy6XY+3atWzatIm+vslPMjo6xujoCCMjo4yPj5PP58nn47nUYcaJq2/biavh1UK7Idp74D9liHJCQ4hyD2T3G6Kou1WvXO5pw3NliFakJEBZs3kNZGBoeGh+QYMn/upUdyW3S5P7W4FTqIUopyWP76BWifJTogJTmo08tYHiGWJ+3AOT9yeIY6vqQFlnXk0pjTPR04B/Jc6OPwm8t+Hjy4Dzifx1N/As4nD5LOD1dZ/3IOChwNXAd4lD6epp1e8T3VxdJ5e7mvjfdnvaS0nBTEHOXGppl3LNb26a55jq+Zo1NU9dI1ypxK2ceqFMfQBTSt6v0NeXZ9myW1mx4gZWrLiB5ctvpa+vWkVSoVgsUCwWmgQqkMvlWLNmLRs2bCSb7UsezQAVxsbGD7T8jI2NUSjkD7T9eBS+hE0Qfw3uBg4lWncqtD88qZoyRDmxbibK3rotjocNUaRmKtRadHZBbndy+NmuqjGp092Z3L6S3D+KWoDySOCPksfvYXIlyvbFXaY6XIVok6wW++WIwO6Y5P4e4jVVHSirAxY7NMkCHyaK0O4EriAy1l/Vfc6Lia6r44FnA+8jgpMLkhtEPvYfRGBSdRbx60Ndq/6yUzfKJHM+Zp730d/ff+CWy03fOF0qlSmVKhSLFcplKJUqlMsZymWoVCJgqVT6DrxfvR9vs0Bm0v3Gz6t/Dsg23G/lbbbp4/39/ZRKK9m//2iGhx+W/NcUWb78tgMhysqVN5LLNa9FLxajyqWZXC7HqlWrWLdu3aTvX6UCExMTkwKVqE6JQKVSST1dEsQVkzuIg8dqeJIhwpOF/F80Y4hSnYliiCJJmoffJLdLkvvHUAtRHgv8cfL4XUweLLtjcZepDldkckvncuBkagNl7yEGnztQdtFDk0cAN1GbFf1F4HQmhyanA29P3r8Y+BDVy8M1ZyZfO2fZbJYNGzbM5ylSsX79OqLGdXXaS9EU6ud99PVlkjkf2ST8yDEwkCObrZ/3ETM/atUQB6uf91GplCmXK8n9EqXSzPM7stm4dZLVq2M/zuHhCQqF1QwPH8fw8PEMDx/P3r1PYnAwLrssW7aTVatuYs2am1m9+iZWrLiTTKaVsoMKUDjo+7d8eY41a9aTzR5yUCA1MZFnbGyMsbFo+ZmYyFMsFg1U0jQC3Apsojb0bIQo3V80Sd1rBWA9lA+HSvJnq28/5HZGK0/fyJQhyvpV6xdrsVLqfL2rl7Tl9b4T+EbcKpkK5WPKFH6rQPEhRYpPKFI5PY57+u7sI3d1jtxVOfqv6qdv99THllJT1XAkCxwNnEiciY8QIco+ogqlyWHv+vXd+7t9sUOTI5k80uhOouhsqs+pbqi0iei2qnoWEa7UO484TL4E+DuaF2u/LLmxefPm2a9ePaWvrzbgNIKQWgVINeiISo/cpMqP6nyOSoWDZnWUyxXK5TKlUrSglEoVCoUi4+MT2BYytf7+YTZsuIYNG64BoFzOMjq67UCIMjR0Mnv2PAqAvr5xVq++ObndxKpVt5DLNenfmUKpVKRUKtIsUs9mc6xYsYzVq1cfFKjk8wXGxkYZGxtnbGyUfD5ah/L5AuWy1QYLqkhcXdtNDKA8gvhjP8zihicZgHHI1lWisBzyxyWVKOWYhdJCiCJJUjOZSobsLVmyt2ThkghRSseVKP5WkeJDihR+p0D+jyPM77u9LwKUq/vJXZ2jb48hilpUYnKLzjKi4ik5nGEPcew1TG1ARhfrhOmajR5JdMVeW/fYWUSB2hoiNHkeMRel0bnJjR07dlQGBwcXdqULYhUwxuCgjWatqm1vW7tVw5D+/oGDdngZGOgnm80dFHhUQ5CYA1JJqjzKFAplxsfHqVTGkpNttdPQ0PgUH7mOVauuY9Uq2LIFCoXNjI2dmNxOYP/+P6b6m33ZsjtZseLGpK3nRvr7dzQdPjsf2WxUDS1fvppVq9ZPev5iscjISG2nn+r8lHw+b6DSbjuJesaNRE94jviDntqPZt3v6mo7T/kwqBwJlCE3CLl7oVSGvmEGRzrx75I0N4PDvt7VOxb09X41taEFfUR1wMOh/PAy+SfmyZ+eVETewuQtjtu125a63zBxcQriItEqohIlQ4Qm24mgZQg68xx7eosdmtwF3Kfu/tbksWafcyexvnXU/hdBzDm5sMnXQHS0f4FoA1rovXm1qDIHBR718z6qYcfkeR9xEjudUqmcbHFbPtDuMjpa9ES2w2QyMDCwi4GBXaxb90MASqXljI8fx9jYCYyNncj+/Y9i794nApDN7jsQoKxYcWPDgNm5qVaoTDTp+ezry9Lf38/mzZs57LDDmgYqY2OjDA+PHNg2uVAoGMLNVYkIT6qVJ0cRkfoQ6Y5Emm4myuiaeGBoELIjUYXSNxa3TL7uVkgqWiRJaqIMXJ/cPk9UXp5EbYvjJwPPSD73JmoBys+I+n5pJhUmb2ucI87e1xGzUL5F181AWezQ5ArgBKK45y4iAHlOw+dcCpwN/Ag4A/g2tb6FPuCZwKl1n/HWJKgAACAASURBVJ8D1hPtO/3EaKT/WZjla74mz/uIwCPmfWTJ5XIMDPQfqPiob3mpzvto1vJSP++jFoA4Z6LXZbPjrFr1S1at+iUAlUqGfP5IxsZOYHQ0KlKGh08BIJMpsHz5rZOqUXK59h05lMsl8vkS+fzBf0EymRh6u3JlBCr1isUSY2NjjIyMMDo6ysTExIFtk6cacqs6ZeIvw25gA3FFZA3xR35+GVl71IcoueQqYHYcKgNQXAmV/mSrY4g/g8kvv76xJFQZTW7jDaGKwYokKVECfpnczifOnE6itsXx6cQZGcANTA5RhhZ7sepI1YGyReJiVRd2gS12aFIEXg18k8g9P038CL+T+PG8FPgU8Dki+9xD7ccY4HHEvJNb6h5bljxff/Kc/wN8YiH/I8SBGR/VwKN+t5f6Vpdq6DEwMEAuF4NR69W3vECEH6VSiUqlnLS+FBgfH8d5H5qvTKbCsmV3smzZnaxf/x0AisW1BypRxsZOYHDwSezZ82QA+vt31IUoN7BsWasDZmenUimTz09MG6hs3LiRQw89NAkMY8BoqVQ+EKiMjIwkzxFtP8XiUkgElpAK8ddkDxGeHEXM0h7hwAzXJSNTjNtUKgC5qFAprkmClYajk0wFMtVAZQz6hqFvIkKVvmqwYugmST2pSAw5uJaYCJkD7k9td56nEZe0y0wOUa7CbWjVszKVSm+ejF555ZWVU045Je1lzNqGDVuBhzM4eHtbnq8x8Khvf6mf8VEfguRyuQNBR7Oqj/p5H9W2l0qlYquBZmXNmuXAdDNN2q9czjExcXRSiRJhSqkUk8D7+sZYvvymZKvjG1i+/Gay2TQnX2UmDSKuDyQrFQ5smzw6OsL4+MSBth8DlcR6YBvRkztK6mWkG9bEjmiDQ204Ij0QrPTX3Rp+WWfKEapkqlUrwxGoHAhV8g6p1YLZsDp2L3SmiXpBx73e+4EHUAtRHgQMEBUr11Pb4vgq4u+nlNiwegNshMFvDnbkcNhKpfJT4lV/kE4cBKuDtDbvo7rbS/1Wt9A8/IBm8z7iyrbzPtSt+vqKrFhxEytW3ATEz0ahcMiBSpSxsRPZvftP2b27OmD2jknVKP39O9s+YHZqFQqFaNUZO+gPU4ZcLse6devYvHnzQRVeo6NjjI6OJLNUxigUCgfafnrG3uS2jujD3UD8gV+8jG7hZACqFStTHLVUMlDJQXkVlNcnwUpdCxDE1/eNJ7v8jCSzVupDlXyEL5Kk7lEgApGriNr9ZcADiVPJhxFVKGcTFSvXURssezUdeaIstcLQpMPkcv0cfvg2jjhi7YGrzI1bnzaGIMWi8z6kuYgBszsZGNjJunU/AKBUWpEMmK3u0vMY9u79PQCy2b0HQpSVK29g2bLb6OtLo8KqQrEYWx4fHKjE75E1a9ayYcPGA/OCqsbGxg9UqUSgkj/Q9tOVbXL7ktsaovJkAxGcdPuBX6YS4cd0w10qmQhTSmuhsgkKuYNfAplCbcZKNpmzMilUyce/JUnqTBPUWnQAlhPVJ9UQ5bnAC6i1/VRDlJ/z/9l79xhJ8vuw7/OrR797emZ39nG7e3ck78E7HnUn8o5HiRJNhhJFWY9QjuRIiWALsGBGMAwYyF+JYgSBEQPRfwliw4CROImMODIiRQEBS5HkWJYUSSSPFHk8Hu9u927vsbuzOzvvmX7X45c/fvXrruqu7pnZnVfPfD+LQlVX/bq6e7YfVZ/6Pk7HhQhBQKTJzFEoFFhYWGB9fVvqfQjCMeC6HarV71Gtmq7nWit6vWupaJSncgrMXk8VmN0+zqcPMBAqeXieR7VapdFo4LpuRsB2u72MULFtk0+FUNnBVNiqYfq6LWAOFM9y6LHSRnpMK/yinUSsLEB4ISlcm45s0knESivbFSgjVgIRK4IgCLNCF/hGMgGUgR9k2J3nV4BfxTj518hKlDMU0CqcLkSazCBa67MVRi8IJxilNKXSLUqlWyws/L8AhGFjIFA6nafZ2PgS6+s/A4Dv38t06TmsArMPShiGEzvzuK5HpVJmbm5uLMKt2+0NCtN2Op1B2+SZi2prYnK2qxh5cg5zkNc6zid1glExqB5Ti8Jo14iV8DzoSyYtaGw/vZRUaQ0L10qrZUEQhJNNB9Pz9C+T21XgBYY1Uf4O8HcxPxOvMYxa+R4no5OdIOwBkSaCIAgHjOdtUa9/k3rdxLLGsUe3++GBRGm1nmd723ROd5x2IlGMSDEFZk9mPGsUhUlB5/Hn57oe5XKJer0+FqHS7we02y3a7U7S6ac/SPs5sTWSWsBbQAW4AlzAHNxJ54D9o6Ldi8pqL9Vq+Uqq1XKKaa2WnT6mjsuhvAJBEARhr7SAv0gmMBGcn2AoUb4C/BrmUOK7DCXK65gUH0E4gYg0EQRBOGQcJ6RSuUGlcgP4vaTA7MVMSs/q6n+EaWwfUyx+kIlGOdoCsw/GbkKlWCxRq9Vw3UdQyrRNBhPZ0my2aLfbtNutQf2Ufr9/MoRKG3gbuAM8AlxC5MlhsOdWy+WcVstJAVtptSwIgnDyaAJ/lkwAc2Qlyt9L1neAVzEC5RVM1Kd8ZQsnBJEmgiAIR4wpMHufQuE+jcb/B9gCs0/SbptolO3tH2Vz84sAuO4GlUo6pee4Csw+GFao9HIyOBzHdPiqVqt43iMjRazDpMNPm2azNWibHATB0bcw7wA3gSXgcjKFiDw5KjIdgSagSWRKBcJGqtVyqiuQbbXstJJ2y9JqWRCEA0ADuInMdZNouWQenjNjQpLvFxt9F6duH8/TPha2gT9JJjBd7D7JUKL8/WR9C9ORx7Y4fhPT9lgQjgGRJoIgCCcAU2D2NarV1wBbYPbRQUpPp/MUOzsvA6BUn1LpZiqt52QUmH0Q4jii34/o98eNilIOvu9TqSxy+fLlzLYwjAY1VGzKj037mVST5UDoAu8BdzGRJ5eBGFNI9uSUpjmbKFIdgXZptRzVgXOJWBndTziMVpFWy4Jw+tEO4CT1l1Kyw85tXaa4gIl4KwxTCrWfTJNOqTS4FbPYmtKWTYXJd8zIRJD6/olGpMuIfJnV76Ut4I+TCUwhdltU9kXgHyTrm5g2yN/CRKJcx/z+CsIRINJEEAThBGIKzH5AqfRBqsDsPJ3Ok3Q6T9NuP836+l8HfhYA379LuXyDSsVEoxQKd05UgdkHQeuYfr83VaicO3eOS5cuZSJUoigeESq9QdrPpK5B+6aHkSdLmJSdK5iTb5EnJ5s9tVp2ErGStFruu0bI6NSbLLfV8qhYkTeCIBwqWjEW3TEqPWIPKBjhob2U5PCN9CBHnFqUHn7uVcwwMiQ1d5I2a9M+717yG+ZPCU1MvxZdhLjCQOTgJK9Rj38XZZ4vQJD6LrJTmNR96oMTMiZdBstxMj/m764N4N8mE8B5jDyxIuWzyfpt4K8Ydue5gfz+CoeGSBNBEIQZwfM2RwrM+iMFZl9ge/uvAeA4LcrltwcpPSe5wOyDME2ogML3febn57lw4QKOo1L3Y9A2ud1u0e32BlEqDyRU+sAt4B5DeaIw8kSugM0mKj6iVsv9sxWSLwiWaaksA9nhMpAdo9EdsY+RHc60B2BQ62ggBNKyI8DY7/hkfA6V5qGLWWswtdFs1Iyf/B2d1N96WFNs4oOpGBPhEgznKim2PZAvedLlkFKO1oA/TCYwhdltFMpLwOeT9ZtkJco7iEQRDgyRJoIgCDOK4wRUKtepVK4D/yYpMHspldLzNKurP8+wwOz7mU49vr964gvMPhimLXsQ9OmMRUMrPM+j0WiwuLg4JlQ6nQ7tdiuppdIZtE3etc17ANzGyJMLwKOYA8YmkoN9Gtl3q+XLyUnLyAdOWi0Ls4ZORz8cQioLYGQHZKIfiIfLbsCZqwOyFxQYWx8/XNHrjNTyISpijiPSomsX8QKHl3K0Avx+MoG5YGEFykvAF5L1GwwFyjeBdx/w7yEIiDQRBEE4NZgCs8sUCsupArMVOp0nBhJla+uvsbn5EwB43nqmS0+p9B7q1BfB1IRhQBgGOUIFPM+nXp9jYeEcrmtPcs3BYafTpd1u02w26Xa7g7bJ/X5/MIYQU+/kPkN54mIiT077n1bIsq9Wy9VkebdWyyNiRVotC3vlUFNZRtJGHiaVRTh+BsIqYmoq424cVcrR7RBuR/DVRLpcDeClAD4VwUsx/HiyrzWyEuX9B39pwtlDpIkgCMIpxnXb1GqvUavZArNOToHZTwOkCsxeH8gUzztb7WGsUMnD8zyq1SqNRgPPy57cdrtdWq027baJUOn3+/TX+/RX+nBOw+OYX9wm0kJRGDJotTwhdW5qq2W7j3SrZStXpNXyqeFIUlms7JiRVBZhNjiulKPrmOlfJTt4tAM/tJZMm/ATSeTofQ++UYZXCvANF+7AMMJlNPrF1nt5iNcizDQiTQRBEM4QSsWUSu9TKr3PwoKpshYE85mUnvX1n8L+PBQKS5mUnkJhaeYLzD4oYRhO7Mzjuh7VamWCUOnRaXZoFVt0LnToqR7BZkC/00drKXwiTGE/rZbjKsTpVssMC1lObbWcCpMXDpYTk8oSS3SHMJscRMrRPeB3y/C7j4P+EDwewKd34NNbZvqZnWRcEb52Dr52Cb6+ALfKjFmSs9zl6Iwj0kQQBOGM4/ub+P4rzM29AqQLzBqJ0mx+gq2tzwG2wOyNVFrPOzjOlLoOZ4QoComi/IgB1/Uol0rUvTpux0XVgY8BPvSbAe2dFq6r6fY6RNolCAPCMCQIA6SKnbArmVbLE9AqKVw70mo50x1kUqvldFegM3KwL6ksgnC6GIhF4JaCW3Pw23PANfhwz0iUl3fgsyvwc3fNfZYK8PUafKMO36jBUnGPKUdkv1tzn8vJ7nKklMJxHJRSKIbLjnIy2zK3UczX5lENxabaRJ+y4xeRJoIgCEKGbIFZBgVm2+2PJhEpT9Fq/WAyOqJY/IBy+fqg3bHnrZ3SArMPxphQ2cR03JkD94pH8XyJBa+KG3tcWOhlLiD3g4BOv0O336Xb7dILegRhkIiVgDCStAthDyjN3joCjbRaHrvKGiRipX0yWy1LKosgCPtCwbslM/3WBUDDk10jUF5uwue34G+sm6G3CkOB8vU6LBce7CEnphy5KOWhcFHKRUFSrN7BUSoRGA5KGamhHI1SIY4XmbkboZwQ3wPHDfE8jetqHE/juuA5CtcFx9V4rsJ1Fa4HruvgOR5KKVzXRQ2i10BrjUKh0Sil0LGZ5/0Zdayplqq4DZfbpdt02jmF42YYkSaCIAjCVNIFZufn/xSwBWafGkxbW59jc/NLgC0wez1VYPb9M1Bg9gHYhmg7JKqFtJ4ASrCjU5EqMbieh+/7lOolPOXhKidJx0jGRNANe3S7Hbq9Lu1eh37QJ4xCwjAgGAgbQdiFB2q1nHMYqXomWmVaq+WJ+95rKksqdWXPqSxWdoCksgiCAKBspIQxESZy4oMy6tY51P+VyIOn2kSf2iJ+cYvoxzfRP78GgHOrgv+tBYrfWaT4nfP461Ucx8FVLso1+3IdF0c5OK6Dg7mtHJWMc1DJ3DwZc5HKVmhRybpMh2g93BZrUNohtp3ZYrMcx4o4Bq2VaXIUxOjAxH2EsUaj6WmI0eYBiVLyO0Q5AcoJwQlxVIhyA5TS5jjOiVDKSGKVCGOlYpRjohB7vR7n6ueO5P/uqBFpIgiCIOwbU2D2VWq1V4F0gVmT0tNuP8XOzg8BoFSPUunmIBKlXL6B656tArNTaQI3gTLQwXTbwcwjLyRyQrPOwxwpJeeRtgOkW/QoVkpUnRoXXdcc/KWItabbN1EqnV6HdqdthEoQEgQmFSgOI5M2rhnOBWGUA2u17Jkw9J3O7qks6ftOTWXpnJ30IUGYWVQqnWMoLdKTo5JtNgWERGgM0kXAcVwjHhwXpRSe44Kj8JRrRIQzFBKOcnFcZeZK4bhuss9EUqTFRAqN2aZjUF8H/XXAiWk/tsb2x5fYfu4O219covdzdwAo3Zmn/r1HqL12her3LuFvVtBodCIqtNbExOjQPFgcx0kKyyH/4Ka/ft3x1Vor0A5aOxD7xLFJQ9LaGa63fwtt75l+ziYWBSdE1V38QgmtfcwBzelBpIkgCILw0GQLzP4RAEGwkOnSs7b202QLzA6jUQqFu2e2wOyADqY18T6JMGKlpzDHMknU73BZ4Xku5UKJulfDK3hQIiNeQiK6YZdu2KEb9eiGHYI4JIiCQTrQ1AO7tGyxc7ssMuZssVurZQ0484CbpLL0ka4UgnCYpIRDUqNiLLoiR1pkRYVJ3XCUM5AVaQHhJMLeygwHB8dL5k4ypdI+gMHvgVWj06Ir7LKNxIj1UESgNVpDTGwiMXSMWW3GxDoiCgDCgxEV3/Mpf+9xyjzORSem+8QG7efv035+mbXP3mDlS28AUPhgjsqrl6h89xKV1y7ibZUe/DEPEaW0iRzhwSOCrUxRqkK/PcdpVAyn7xUJgiAIJwLf38D3v8Hc3DcAiOMC3e5HBik9zeaLbG19HgDH2aFcfjvV7vimFJjdD1MvsGvC5N8klHJwXZeaV2feWzB5zYmE0coEBoRxSKfXpdPr0Ol16AU9wjgkiAOCKCDUgTmq8BhGxjgM19n1+zk5Fhlz+lCYgoe7dQUShFOC63o4yqFYKA0jKBhKi9zoiuQL2PNcFE5KWCRiQtkoC3AdD+WoQeqHp1xQyW1I1adIyYkJ0RUk48fSREiJith8EY+Ki1jrJH0kERX9yIgLrdHTf6RmFhU7lG+cp3zjPOd/51m0E9N9cp32C0aibP34u2z+7A0Aiu82jEBJJIq7UzzmZ39wmABXjXKiU3sBTKSJIAiCcCQ4Tp9K5U0qlTcBc1DW7z+SiUZptT6RjI4old5PSZTr+P768T35U47WMWEYE4aTO7A4jovneTT8BudK54ZiJUW326PX69HpdOi2OvR6/SQFKMi2bE5Hw1iR4kxYPypdRMYIgnCMOI6Lm3wfuo6L53p4rkvBL1IoFCh6RQp+gaJfwHM9amVzctzsZgt9p+tTZBLRUtu01sTaRlAMJYUmKypiYqIoRIfQ131zH/kCO3JU7FC+vkj5+iLn/8+Pod2Y7lNrtBKJsvmld9j48nWIofjuvBEor16i8vpF3OYDFpYVjgSRJoIgCMKxoBQUi3cpFu+mCsxW6XSeHEiUzc3Ps7HxkwB43lpGopRKH0iB2SMkjiP6/el/b9c1hWvL5TKe5yWV/4doDd1udzB1Oh36/X6mxkocP8T/qcO4fDkIGZM+o5m2DOPSZdJcEIQTgY208xIB4roenufhex5Fr0ShUKDgFQZzyHe0YRwRxzFRFBHpiHa3YyIuYpOWsdMeb0kvnG5U5FB+8wLlNy/Av34O7UV0PrpG+/ll2s/fZ/Onb7DxN94yEuWdBapJJEr5exdw2yJRThIiTQRBEIQTg+u2RgrMuvR6j9JuPz2ISNnZ+WEAlOpSLt9MiZQbuG7rOJ/+mce2V+73J6dWeZ5HqVSiVqvhed5YtEoUxYNolU6nQ7fbIQhMlEoQBARBgNYTQr1tpMhBkydj8iJkrHSxEsYuO4BPVsqAyBhBOCSs/EhHhPien0SAFIcixC/gOs4gHWWAgjjWAwESRRH9oE+n2x4OtHWkRrHrbNFNn8P5XhJmDhW6VF6/SOX1i/B/QOxHdJ9ZpZVIlI3/8DrrP/8mRIrS2wuDdJ7y6xdwO/5xP/0zjUgTQRAE4cSiVESp9B6l0nvAHwIQBOdS7Y6fZm3tZ7FHp4XCnUw0iikwe2xPX8jBpun0JnoVhed5VKtVGo0GnueOjQjDMBWtYuZWqNiOQAdqEE6qjMmLkNkrImNOL9NO6tWEcXtZt5f95+0jb58w1hxp2jZH2SgQF1cZEeI5LsVCCd/zKXpFI0NcH88zH4RBZ5TULqMoIorNFMYhvbhnq1jmP779TNnz1dHPQ7qm6Ojy4EGT+9dTY/rA5GxI4YzgBC6V1y5Ree0S/O8QF0I6z64OIlHWf+4t1v/mG0aiXD9H5buXqCYSxenJafxRIn/tGcTUW8pegpKTAkEQzgq+v47vf525ua8DEMdFut0PJ62On2Zn51Nsbf0HgC0we4NKxab03MRx+sf59IVd0UkNlMlnFEo5eJ5HvT7H/PxCrljp94NUtEqXfr+fkirBsL7KcXJWZYybLOd0I57Vk/rMumnbHmb8tG3xyNyO06l16ZP6dC0fTf4JfzyyvNf9jz5Ozv2GKTGmHojreniuSYkpFUv4SU2QQqGI7/mp9qjJS08+vmE7lRITRbTCNjqOM4+VmY+uHx1zGIKwnsw7mM5llWRdLTUmxIgUiUg50zh9j+qrl6m+ehmAuBjS+djKoDvP+s+/wfovfh8Ch/L181S+e9FEonx/Eacvp/WHifx1Z44Q1+0TRTWGRwPmp2Qoyqf9Kk8iLWEm/YorlNK5Qj67n7wB4z3GhqIn7xdtuG5v44a3x6s2T75fduy0cQiCcEJxnN6gwOz580Yq9/uXB3VROp2nWVn5ZDI6zCkwu3Gsz1/YP1rHBEGfIJgswGx9lVKpZMLzXSd1f/O93u326HaNVGm3h/VVTCqQSTWaSU66jPGTZRsQdAJP6seeT96hRV5UQd4+Rscf5D5ODKbTi60H4rouruvi+z6FQoFSqWhESNGIkHS9o3RESBTFQwnSjug1e7SjU5J2GQLNZLqP+dwUMSKlhhEp9vMUYSTKjH4FCQeD0/OofvsRqt9+BIC4FNB+bihR1v7j77P2n7yOChxKb54fFJYtv7mIE4xfTBAeHJEmM4ZSPebn32R7+4Pc7bZPdjI6NZ8kVtTY+OyY8X3l72Pa4+RfyslGzDipsel1EMfj69KXp7L7sLftZNeln4tKXoeTrHdSz9fuXzH6fE6rlBqO3ZuUMuP3Kpv2LqU8z6VerzA3V6Fer3Lp0jzFos977y2ztLTK5mYTQdgLSulUgdk/ASCKakmB2adot59mc/MLbGz8dQA8b3UgUSqV6xSLH6CUXO6bdWx9lWm4rkexWKJarXHxojtWuDaONd1ud1Bjpd1uZ4rWhmH4cIVrZ42DkjELyVx85YnGdsxy3fTcpVgs4fs+xWKRYrFIoTBMibFYEaK1/SwaERIEId1ujxNsf44ODXSTaTNZ52NESpXxaJQAI1LkT3dmcbo+tW9dofatKwBElYDOc/eHEuWXXmftl7+H6juU31gcSJTS9fMiUR4SkSanjMknv+ntwoNycFJqcmzwrEopx3Go16vU69WB+JibM1O9Xk6tK9NoVAaCZG6uTL1eoVqd3q++2exw584qd+6scPv2fZaWVrhzZ5Xbt1e4c2eFnZ321PsLZxvXbVKrfYda7TsAaO3S7T6WRKM8TafzDDs7nwFICsy+M4hEMQVm5f11GrFiZXp9FZdyuUS9Xhs7MQQIwyipr9IZ1FmxUsVOcpYjnAQGKTGeh+dZEWIjsrKRIIXCeNFJK0LC0KTC2IiQVqs9uTizsD+CZGoCy5jDLBuNMoeRKPYQLEzGSjTKmcVt+9ReuUrtlasARNU+7Y8bgdJ+4T6rv/wa/K3XUF03I1HKN86hQpEo+0GkiSDsg9MspZRSVKtVarUa9Xqder3O3Nwc9Xp9bF36tp1qtdrU/UdRxM7ODs1mk52dHXZ21rl16/1kOT2Z7UEQEQR9arUFHnnkUa5ceZRHHrnGlSsXefnlZ6nVypn9b2+3uH17ZUymGMmyQlta/QkplIool9+lXH4X+APAFph9epDWky0we3sgUSqV6/j+vZn+vAt7RQ8K107C1lep1erMzy/guu7YeyMMQzqd7qDGSq/XG0Sq2BorgrB/xlNijBDxkiiQwsSUGIvWEMc2JSYcdK9qt09JSsysE2NqoXQYRmYVGEajpEWKxkSiSNmuM4vbKlD/+jXqX78GQFTr0f6BlET5le8CoLouldcvUHnVFKEtXT+Hip1puz7ziDQRhFNEuVwekxm7TbVabSBCHGf6F+ao4FhaWmJ7e3tw2wqRvHXtdhs9Pfcog5UwzWY2LUdrRRwXqdUu8MgjH06mq1y9ep5r1xZ57LErfOYzz1OpZCNXNjd3EpGyOpApw2mVTmdyi1ThbGAKzH6NubmvAabAbKfzkYFESReYdd2dTF0UU2BWTnzPIsP6KpPH2DSHRqPB+fPncRxnTKyY+irdQdRKr9cfCJWZrq8i7AvXHdYDSYsQkwaTjQTJi3wCk1YWx5GkxJxWrBjZAe5h3H4RKDNM6bESxdZGOUNZhMIQt1mk/pePUv/LRwEI57pDifL8fVb+zqsAOG2P8usXBi2OS28viEQZQaSJIJwgisViRmTkyY307dHoj0kHUJZWq5URGcvLy7z99tup6I/JU6vVIo6PP/xWKY3rdul0bnHz5i1u3vzTgUiJ4xJhWCeK5mg0LnP16iKPPnqea9fmuXZtgWvXzvPkk1f53Od+kFKpkNnv2trWmFCx0SpLS6v0enJCfNZwnB7V6htUq28AtsDsI5kCs83mi8nokFLpvVRKz3V8f3PyzoUzRRxH9PvTz1pc16NQKFCpVPA8bywqQGtSbZZNxEpaqgRBcLbqq8wINhLJ1gOxKTFZAVJIpvGUGEs2JSak1QokJUYwREA7mdaSdcVksgVmKwydWQ9pd3xG8bZLzP35Y8z9+WMAhI3uQKC0n19m5VdNCrPT8il/z0iU6quXKL47f+YlikgTQThATAvM+q5yY1LUR6FQmLr/brebERkbGxt88MEHuwqPZrNJs9k8GS02DwErUly3OzhRDcPv8+67Jd55p0QY1oiieaKoau/BxYtlrl2bS4TKRa5eXeTatYs8++zj/NiPvTh28LqysjGW9mOnpaU1guB0/m2FIabA7BLF4hLz8/8egDCsDQRKp/MUm5s/liowuzJodVwuX6dYvCUFZoWJ2Poq/f7kqDfP8yiVSgNJno5WsWkWtmitabXcyRStDQI50X54VEZ+2EgQWxi1QGicaQAAIABJREFUUPAzImRaSoyRICYixHRwkpQY4YDoJdN2cttjPBrFYmujiHM9c3hbJeb+7HHm/uxxAMKFzkCitJ5fpvXpJVYAZ8en8tolKq9dpPLqJYrvzaP02cpRFmkiCClc1x0THfuZSqXS1P0HQZBJXbEpLnmpLenoj+3tbZrNZlJQUNgLRqR0cN1O0lL2Flo7SURKmc3NGmtrDf7qr2rAmwA4TohSPRwn5OLFea5evTCQKVevLnL16gWef/4JvvSll/H94ddnHMfcv785JlOsYLl3b50wlKOR04jnNanXv029/m3AFph9fCBR2u1n2N5OF5h9O5XW87YUmBX2ha2vMr1wrUe1WqXRaOB544X+bH2VYSpQN1O01sj1s5XGkZYf6dSYUqk4SIWxIiTvbwrDlJgwNNEgQRDQ7XY5a39L4YQSJlMLWE3Wlci2O/YYtui2BWmFM4W3UWbuTz7E3J98CIBgsU37B5JIlBeWaX7mNgDOdsEIlCQSpfBB49RLFJEmwqlCKbUn4WHHjBY6rVarU/cfhiHNZjMjPlZWVsbkRlqKpNf1Jh/pCkeAUnFKpKwDJCKllKT2zBFFcwTBPHfuwJ07KzjOHZTqZ+pVOI7i4sWFjEyx04svfpSf/unP4LrDMMYoilleXh+RKcNUoOXldaJIrv6eBkyB2ZuUyzeB/wetIQwXE4FiIlLW1r6MSUKPKRTuUKlcp9d7j0rlA6LoHo7TlCKzwgOiCcPphWVtusjc3BwLCwu5EqDfD1LRKqblcrpo7UmPWsymxHiDYqk2JSbdMjctwEexKTE2IqTVakmkjnB6GG137GEkSoX8aJQ+B9NyXJgZ/NUKjT/+MI0//jAAwYXWMBLlhWWaP2IkirtVpPLdi5x74xqL7xXRp1AWq/0UZjxNfPOb39Sf+tSnjvtp7Jtr167x0ksv8cEHHxz3Uzk0qtVqblrLXlJdqtXq1GKmcRwPpMde6niMTp1O5wj/EmebSYVgjwKt3ZRIqROG88RxGXMJRuE4vUSk5J84eJ47JlWuXTNS5cqVRS5fPpd5n4ZhxL17ayOpP6sDwbKyskEcn83v6tOIKTD7RKo2ylPE8VDYKhXgeRt43mYybYxMZp3jtEWuCIfCeDHS8d9VU7i2k6SVdOj3+wOhslvh2oUF8/2+sbHX7/dsSowVIsOUmEIiQMztvM/FaEqMjQiROjDCYVOvmyjknZ0Z6+KnGLY7thLFTdbbArMn258Kh0z/YpP2C8uD7jzhhTZOz8N/vE5veWP3HZwwtNbfAl7K2yaRJsKBUyqVMiJjtzoeo9Efrju9b/io7Lh79y43btzYUxcXc5VITj6F6SgV4botXLeF75uqalakRFGZKJojDOcIgjmMSNE4Tj+RKeZgfGlplaWl1dz9+77L5cvnMzLFTj/6o89z6dK5zPh+P+Tu3dUxmWIFy+rqlryvZwhTYPb7VKvfB0yBWd//MJ3OFXZ2qoThPGG4QBgu0OtdpdV6LiNVLEr1UlJlVK4Mb7vujB2oC8eOra8yDdf1KBZLVKs1Ll3yxkRFHOtMClC73R4UrS0UisRxRKFQzESEuK6bSokZipC8aBitQeu8lBi5uCEIB4JmPBrFZ3K74wAjUuRw5MxQuF+j8Ec15v/oCTSawocD4qc83un/4XE/tQNHpIkwRqFQ2FOL2kmpLrt1cGm32xmRsbq6ys2bN8fqeEzq4BJFclVIOHrSIsUmBGvtJSKllIiUeeJ42OrYcXoDkZImCCJu3brPrVv3cx+rUPC5cuU8V66kpYqprfL5z3+CCxfmM+N7vT5LS6sTWyqvrW3nPo5wMlBKUy4vUS4v4fv5giOOCxmZkl1eoNd7jFbrhSQianT/3YFA8f1JcmUTx5H0QWHvWLEyvb6KS6VSZm5ueGygNdTr5nuy2czeWWsG6TBmCpO0VjkLE4QTga110gSWAYdhNEoDI1McpN3xGUShKC3PUW5f4x1EmggzgOd5YyJjWh2P0alYLE7df7fbzciNra0tbt++vaf0ltPcwUU4eygV4rpNXLdJWqREUSmRKQ3CsJGIFHPQn45ImUS/H/Dee/d47717udtLpQJXroyn/Vy7doHnnvsw587NZcZ3Oj3u3FllaWkYoZKOVNncPPoUKGF/OE6fQuE+hUK+aLMYgTdPEOTJlXk6nY8QhgtoPf497zjt3EiV0eV0fR9BmIweFK4dJY5nNF1BEIQsMdBJJpuNUWByu+N+MgnCjCHSZIZwXZevfOUrPPPMM8RxPDESpFwev9KYJgzDsQ4u9+7d2zW1xS73+/JtJwiTUCrE85qYyzBGpMSxl6qRMk8YzqF1AVAopZOOPf2pIiVNt9vn5s0lbt5cyt1eqRQH6T5GpqS7/zzJ/HwtM77V6oyl/aQFy/a2dHiZFUzr7XsUCvnCDWxth3ImUmUoV8y803maMJxP3qdZHKc5FqUyjGQxt113c2LNH0EQBOEUY8XIDnAXUwdF2h0LM45IkxkijmN+/dd/HWBMbqyurua2qM2L9jAt8ARBOCocJ8RxjEgpFNIipZyqkTKP1uYrWSkSkdJDqf2Xqm+3e9y4cZsbN27nbq/Vyqk6KiZC5coVc/ull56hXq9kxu/stHNkyiq3b9/nzp1VWi2pITBLKMWgi1SxmC/ewMqV6kCsmOiV+Uz0Srv9McJwnrzDCdfdnihXhre39iwLBUEQhBkkAtrJtJassyk9tjZKOhqlh7Q7Fk4cIk1mCK01zz33HM8+++yp7p4jCGcBI1J28LwdwKRcxLGfpPVUktSeObT2AZ1EpPQfWKSkaTY7vPXWB7z1Vv73yNxcZZD6Y2XKtWsXeOyxS/zwD3+carWUGb+52cx0/bl9+z5LS8PaKu221MqYRYxcMXV8isV8AQemkG0U1SZGrZiaK48Shg3MJcc0cSJX8sXKMHJlC6WkroUgCMKpoJdMW8ASw3bHJYYFZi0SjSKcAESazBitVuu4n4IgCIeE4wQ4TpCIlGXAFAC1IiUMG0TRHFqbnn9KRSmRcnAnlNvbbba33+eNN97P3T4/Xxvr/HPt2gU+8pGrfPazL1AuZ+tlrK9vpyJVhhEqVqr0enJJaZZRSuN5VgBOFvpGrszlyhVbg6Xb/RBR1MBUEkwT43lbE+qsDG+77o7IFUEQhFkjxGQ128zmdLtjWxsl3e7YFqQVhCNCpIkgCMIJxhSO7eN52xSL95I2m4UktadCGM4lIsXDRKTEiUTpH9rJ4+Zmk83NJq+//m7u9vPn5zJtlK1UeeaZx/jCFz5JsZitk7GysjkmU27fNqlAd+6sEgRSG+M0YOTKFp63Bbw3cZzWDmHYmBi1EgSLdDpPJnJllHCKXEm3YW6OtcgVBEEQTgh57Y5tNEqF8XbHIaaOysMF4grCRESaCIIgzBCm3okVKVsUi3cTkVJMRaTME0V1tHawESmHLVLSrK1ts7a2zXe/+07O81csLjYyMsXWVvn4xz/CF7/4MoVC9qdpeXl9LO3HRq7cu7dGEEjM7mlCqRjfN6k509DaTcmV8W5BQXCZdvsZ4rie8xgBrrs5SP+ZFMHiOG2RK4IgAEbomqLu5ZH5+LooKqG1ue04JRwnIIpaOE4H1+3iOF0cpzMyH1/3sOm4p4p0NMp9hu2OiwwliouRKDFGosg1F+GAEGkiCIIw46QLx46LlHJKpMwlIoUjFykWrTUrK5usrGzyne/cGNvuOIoLFxYyMsUKlk9+8ml+6qd+GM8b1sWIopjl5fUxmWLny8vrRJEcdJ5GlIrw/XV8f33quDj2p8qVXu8qrdZzxHE15zH6OUJlPDXIcToiVwThhKG1SkmN3WTH6Pbi2La8bmL5RBnx4XkBcVwgDIf7HK/vlI+5SDIqVHYTLpO2d09X+mK63bGNRikkk03pSddG6WNSek7Rn0A4OkSaCIIgnEKyImWTYnEpESml5CpYLVUjxcGk9kRJ6+PesZ0AxrFmeXmd5eV1vvWtt8a2u67DpUvnxrr/XL16gU996ll+5md+BNcd1sMIw4h799YyNVTSBWvv398gjuUI6jTjOAGFwuqgc9UkzEnNfK5YMXLlMVqtF4jj8th9leqOyJXNVCHbtFyRosiCMIl01OQkyRFFexEfxURylHZ/UABMWuuoaPD91T2JiNFtSgWZ39B63TyPnZ1u6nX6OXJmcuRKNoqlRhBcyAih8TpQ+SiV95zzl1130mvvJa/z+I4VJmLbHTeBexg3VcC0O57DdOsxhzymNkofKTAr7AmRJoIgCGcEI1K6yZWvTYrF28mVOHuQWiMIGkmXE4VJ7QkSkdI/EQdHURSztLTK0tIqr7zyxth233e5dOkc165dzESpXL16gc985ge4eHEexxkeXAZByN27awOZYiNUrFRZXd1Ca5EqZwHH6VMo3KdQuD91XBSViKJh8dpR0dLtfoQwXEDr4th9Hac9NR1oKFekwqFw8sme/E+O0NhPdMfDnPybz87dPZ78D28fdcSl+S0ODuxz/rCyKQzniePLqYiah5NNe4162U02HQgRw2gUG5RYYNjuuE623bGVLoIwgkgTQRCEM4xSGtft4rqm2lpWpJQJw1rS8WQ+dZ8wSe05hAOchyQIIm7fNvIjD9/3uHLlfG6h2s997ge5cGEhM77fD5IitUOZcufOsGDt6urWUbws4QRhPi/3KBTuTRyjNcnnJy8lyMw7nacJw/nckH/HaeV2B7LRK667mZwgSsK+sD+0dpO0zWkiY+9RDw+TZuK6TXx/ZR8n3MMT9FOVZvKQpCNLTQ/fh+PB05rMFASLB5LWtLc0pPFtpmZMB6UmhJBYMbIN3MW8hYuYaJTRlB5pdywkiDQRBEEQMqRFii3GmT6IMiJlPhEppnS944RJqO7JEylpgiDk/feXef/95dztxaLPlSuLYy2Vr169wLPPPs7589mOLd1uPzftx0qVjY2do3hZwglDKXDdDq7boVhcmjjOyJVqqnitlSrD6JV2+2PJZ238kM11dybIlXQEy9bkkwfhxGO+e/eavrH7Sa7W/h4fOcw9cfW89ZGT070UNO3Je3CGMMcA5vvrIDCibrc0pMnv3SCYTySfWb/X01cTzbNXCTMSMVPs4pS7OPUOznwXp9pBOXpYYFaCAc8cIk0EQRCEXUkfRBmRcivVSSAtUhawca6OEyRhzydbpKTp9QLeffcu7757N3d7uVwcS/uxtVWef/4J5ueznVpare6gdXJapthpa6t1FC9LOKEYudLCdVsUi7cnjtNaJXWI8qNWTM2VR5PUutEr//GIXJlU0HZbOnUcANmUx4crPGokx3iaVz5x7hV439/e59V7O5coJuFgUCrCddu4bvtA9hfH3i7icPLnLYqqY5Ewe04Jc3o4bhfH7+AUujheF8frmHX2c+R1zHo3ZzmzrifRUjPGcUiTnwT+B8yv+v8E/Hcj24vAbwIvAmvALwLvAR8C3gBsZcCvAb+WLL8I/K+YwKrfA/4BUhtZEAThUFEqHhwImQ4mH2RaMoZhPZXaY6yJLTQ7qwfknU6Pt9++w9tv38ndXq2WM1LFRKsscuWK6f4zN5ft0LKz0x50+bl3b43bt1dZWdlgZWWT+/c3uH9/g+3tgznQFGYXpTSet4Pn7QAfTBxn5MpcrlyxNVi63Q8RRQ3GTxRiPG8rt6BtenLdnVN1sG/qQRT2IDlGT77S6QfZq+h7Zby9bBfPWx+kF+xHcpyUulOCcNg4Tojj2N7DD0f+538PKWphiTgsE+kGgb5k1ifr9vw6XCtQkvlguZezLi1exiWMcvb++VdK4XseBd/D9z0Kvo/vucncrvOSMf5w7Nh9Rsb5LpVSCcer8Mtf/ScP+D9ycjlqaeIC/xT4InAbeAX4KvD91JhfBTaAJ4FfAn4DI04A3gF+MGe//wz4u8DXMdLkJ4HfP/inLwiCIEwjK1LWABuaayNS5gjDBkFQx7hthW19PKsiJU2r1eH69Vtcv34rd3u9XhmTKdeuXeDRRy/yyU9+lHq9Mnafbrc/EChpmZJevn9/k1brYEKphdnFyJUtPG8Lc70pH62dVBvm8aiVIFik03kykSujhMljTC9o67rNQzmJHxYf3X/9jUnb9158tDcmL0xtmb13JBnO5UqzIBw3ph5MH8exRU4eAh90QaFLBVStilus4cRVVFxDBRUIKuiogo7K6MhIligqEQUlwqBI2J8n6F8k7Pv0WwV6XZ+gv7dTdcfRVKox1WpMtaqpVjX1OsmkmJtTNBpmmm+4qW35U3GvAW5AHMf0g5AgNFO7ezpzl45amrwMvA3cTG7/FvBlstLky8B/kyz/NvBPsJco83kE00Tqa8nt3wR+DpEmgiAIJwITmmtSEEZFShSVkyvjDYJgDiNSNI7TP5V58Ds7bd58833efPP9zHrbkjIIYi5cmOfixYVkmufChYXB7Y9+9DE++9kXqNXGr2a1Wl1WVoYSJS1W0us7HWl7e9ZRKsb3NwY1iyahtTtWYyUrVy7Rbn+UOK7n3Dsckym+b27HsYmearXG63VkC5Tmi4+HqWlgio+OtpLdW9FJSV8ShJOB4ygT8VDwk7mXue377sRtw9uj98mun7z/6fsuFPZaN2h3ogiaTVhbD9nYjNjcDNncjNncitna0mxtaXZ2NNvbmp0mNHcUzZai3VJsbDncWXLotF06HZdOxyEM9la42XEivEIPz+/j+j1cr4ubRLgotwNOB+W00aqNctuDiJhqNabSyPs9mH2OWppcBdKX324Dn54yJsSUgT6f3P4w8G2MCvyHwJ8l49OJwLeTdVNxXZeFhYXdhp04Go0G//gv/oJeTw56hdON65ov9ig6XSfNwjQUaAeNQmsPtItOXQFWxICGU3h11nXN64yi2MRUTmAjmZxaFf/yJTM9cplCMp+7fJHzly/z/LOXKXzhEziVcbkSbW3Tv7dMcPcewfJ9M09u9+8uE9y7R3DvPrrbPZwXK5wOHEzrzgL0dJE1fYEVfZmV+BKr+jIr+hIr8WVWg0us9C+zEn+UTUzkyt38kkG4hFRoUlEtqqqZLK9TVS2z7Dapeq3BmEoypposV2madapFlSa+mnLFM04mQThkMt/vM4TyfVSxgCoUcAoFVMFHFYqogo9TLA62m22F7PpCwWzzfVQxuY8dVyyg/AJOcbhPp5Dcp5Csz+zD3ifZf8FHeQd7CqujCN3rE/f76GQyywG610MHAXG/i95KlnvDcbrfJ+j36fcDmr0ecRCgexP2EfTRQd8shz10GAwfr5vsr9dP9mHuo/vDHsjzybRvku/qUHu0dI22rtHSVdqD5RptXR1sM1OFdr9Gq2dv2+2Lg+WIcUHken0uPvobdE9ZpYxZKgR7F3gMU+fkReD/Bp7b5z6+kkwsLi4e6JMTBEEQHhYNKkJh2hobsiJFaxf08ErJaRYp04ibLXpv36T39s2p45y5OoXLl/EfMVJlIFouX6LwyGVqL7+E/8glnFJp7L7hxgbB3WUjVO4tD4VKer58P3NAJ5xNiqrHFXWbK9ye2oG2q8us6ousqUcAKMU7KTnSokhX6nIIZwfXzUqCYlYeGNGQSIK0PMiVGEZEGIkxXJ8ZWywmEmNcWozvY69tgvdO3OsZgWBlQs8IBCMgAnTfbA83t8blQT8YGxv3U8KhZ0SEHRsn+zL76A+Wh/uwUsPch/gYhZaTTC7Z70/NgVfo9FRIQ23SYPOh96U19ClmBEyXOv/sR36B29/f/f6zxlFLkzvAo6nb15J1eWNuY55fAyNKNGDDK76FuRb3dDL+2i77tPzzZGJ5eVlvbEwPSz2JVKtV/qvPfIYPPphcCE4QTgO1Wg2AZvPhC30JpwtbOd+k9jQIw7mkw4RO8pN7SWrP7FzVs+k5OzuHEN3RwiTGvr0OrGNqqmdpNKpcvLgwSAUyKUI2TegKF595jsXFeQqF8cOGjY2dVG2V0VorJiVobW2LMJSoMcEwfL9XgEvH+2QE4QEoFHzm52ssLNSZn6+llussLNSYn7frzbxY9PE8N5PKYSNQDoowjOj3A4LAzPtBSJBM/X56OSDohvTXmsPbgb3vcKy9PW1b9nZEEATjj5Xs4+jxk6k6vimJvDiRFIAS5mnPYV6CwpwJ95PphFKvlCjXb7CxuUl3Bs+zp3HU0uQV4ClMms0dTKHX/3RkzFeBXwH+EvgF4N9h3iYXMEd7EfCRZD83k3XbwA9hCsH+beB/POTXIQiCIBwTtnK+5zWBFQDi2B8RKQ2T4oNCqTgp9DZbIuUo2dpqsbXV4saNyW1vlVLMz9cG9VWGtVeGdVeeeupRFhcbeF423CCOY9bXd1L1VTZzRcv6+vbMhbALgjDblMvFlPwYlSDjMqTRqFGtjkfnWZrNDpubO2xuNtnY2OHu3VV6vYB2u5srFEbFw+j6vYmNkDg+WxGXpxYrRrYxeRYuRqKUgDpQYyhRQiDAnB0Lh8pRS5MQ+PvAH2DeAv8CeB34R8A3McLkfwb+Jea62DpGrAD8tWRcgMlC/bVkO8DfY9hy+PeRIrCCIAhnCscJcJwgacl6H7AipTwSkeJjIlJ0IlK60sFij2it2djYYWNjh7femhzt6DiKc+fmMmLFSJVhgduPfexDnD/fwHGyV1qjKGZtbSsTpWKL2KYjWNbXd9Ba/t8EQchSq5VHREc9I0AajVEZUqNYnBxysLXVGgiQ+/c3uX791kCGpOdmMstBkO0Ed6iRhMLpJ8JEjLYwuRdgBEoRI1DqmDNgGEajnM4GNsfKcdQ0+b1kSvNfp5a7wN/Mud/vJFMe3wQ+/vBPTRCEk4Druvi+j+u69Pt9giCQEyRh3wxFyjawDEAcF5KIlCphOEcUzZk6KSiUilIRKfJ+e1DiWLO6usXq6tbUca7rcP58Y6xbkF1+5JFFXnjhSc6fH297GwQhq6tbmciV8bSgDTY3Jb1PEGYRpRSNRnUQ9WEiQIbRHqNpMY2GWfb9/FObKIrZ2moORMedO6u8/vq7A9mRJ0G2tpoS+SacTLrJZH9mPYxIKWNSekajUfpI4euHZJYKwQqCcMJxXRfHcQbz9OS6LmoPFf7iOCYIAlzXJQxDHMeh0Wjg5VRKD4KAMAwJgkDEirAnTCvjPp63TbF4F61B60ISkVIhDBuJSDEREErFiUTpi0g5YKIoHsiN119/d+I433c5f76REisLGdHy2GOXefHFZ1hYGG9z2O8HKZmymUkNGrZh3mB7u32YL1UQzjSu62QiPLK1QLIpMHZ5bq46seZHEISDqI7NzSY3by5NiPoYypDt7bYcIwinlxBoJtMKRpgUMSLFRqN4GIkSYyRKmLsnYQIiTQRB2Jfs0Frnyo84jgnDkH6/PxAZNkrEzqMomjjFcUwURYODGtsS3BZsttEnhUKBQqGA7/tUq9XBNEmspKVKGIbEx1khXThxmMKxVqRspURKMRWR0iCK6klECigViUg5QoIg4t69de7dW586rlDwWVzMypV05MoTT1zhh37oORqN8aKA3W4/U18lr+7K/fubtFqdw3qZgjAT+L43kB2jaS55MsTUAMkpxJnQ6/XZ2LDCw6T+peuBWAlit29sNOVzKAi7oRlGo9hGOT5GpFQZ1kaxBBiRIoc0ExFpIggzTFp2KKUy0iMtOyaJDhjKDisW0pLDLu8mOtKy47Cwj9PtTs4JniZWKpUKc3NzIlaEXUl34DEiZSkRKaVEpFQIw4VBRIrWtjhtX0TKMdLvBywtrbK0tDp1XKlUGEsJSncN+uhHH+Ozn32BWq08dt9Wq8vq6mZGpAxly1C6tNu9nEcWhJNFqVTILXg6uRhqjWp1/HNhabW6GeFx69b9geiwkR+jMqTTkc+KIBwJQTI1MRnLDsNolHoyqWSyBWYlGmWASBNBOAZGIzryZMc00WEFhY3syJMdVgAct+w4Sh5WrJTL5YFYGf37i1g52xiR0sVxunjeZkakRFGJOK4RhqbYrDkS0SMRKcf9CgRLt9vn1q373Lp1f+q4SqWUESo2asUKl49//CNcvLhAuVwcu2+z2Znahtne7vWkWp9wMFSr5YlRH+nUl3QKTKk0uQDq9nZrIDfW17d55507I8JjKEPsutECqIIgnGBioJNMtjtwgWE0ymhtlBPe7viwEWkiCPtgN9kBTBUdVoakZUe32x1LacmTHWnRcdpkx1EiYkU4KNIiBTYpFm+jtSKObWpPnTCcIwwbGJECSgWpiJRjffrCLrTbXd577x7vvXdv6rharTyWEnThwlC2fOITT3Px4nxuh46trVamtko2cmVzMJeT0bODUop6vZzp/mKLnI6nw5jCqI1GnUIh/5A+juNBB5iNjSZ3767yxhvvZeTHaArM1laLMJQepoJw5rBiZAe4h+l1W8QUmB1tdxwlY8/IV4VIE+FMMJq+slfZMXpSnI7m6Ha7Yykto7JjVHSI7JgN9iJWHMcZSJVpYmUUESunG6U0rtvFdbv4vkkkNiLFpPaEYS1pfzyfuk+I1grpETibNJsdms0ON28uTR3XaFRT7ZdtxMowTejllz/G4uJ87snvxsbOWKTKaPTK6uqWnOieMBxHjQiPYfeXdNeXdHTI/Hx9YgHUMIwyouP99+/x6quTur/YAqgt4liOOwRBeAAioJ1Mtt1xkfx2x2AkyylFpIlwohmN6BiN9FBKjckOKyV2kx022kNkh/AgxHFMt9vds1ixkSu2vspeaqzYuYiV2caIlA6u28H3N4BbKZFSJgxrwCWiqEEQlHLuH6NUCMRJW+QIpeQ9MWtsbbXY2mpx48btiWOUUszP18Y6BKXThJ566lEWFxt4XvboNI5j1td3Rtowjxe0XV/fljaqD4Dvu5laH5O6vqRlyNxcBcfJFyD9fpARHTdu3M6p+ZGVIc2mFEAVBOGY6SXTdnLbYxiNcglTB+UU/sSINBEOhQeVHaPrRmVHOoVlVHbkiQ6RHcJx8jBipVwuU61Wc8WK1pooikSszDBZkbLl+10qAAAUAElEQVROpbKO1gqtu2jtobWL1h7gEceFRLD4aF0kiipo7TMsc69S+zVSxQiWMJErkaQCzQhaazY2zInyW299MHGc4yjOnZvLiBUjVYa3P/axD3H+fGPspD2KYtbWtkZqrWyOpAltsL6+c2p/P4tFP9P9ZVLXFxsVsrBQzy0MbGm3u5k6H3furGTkx3gqzI4UCxYE4XQQJlMLI1PKyfyUIdJEyJAnO0a7sqSZVKw0na4yTXZMEh0iO4SzwkGJldFuSYCIlRlDKY3j2PL20zGCZShWrGgxgsVPOv34RFERKCTpP9nvVNPlZxi5Moxmke/ek04ca1ZXt1hd3eKNN96fOM51Hc6dm5vYhvny5fM8//wTnD/fGLtvEISsrm6laqvktWHeYHOzeZgvdVcqleKuUR9ZGVKjUhmP6LLs7LQHomNjo8m7794diwBJd3/Z3NyRgr6CIAinHJEmp4S8wqSjty156SuWdI2OXq+XqdexF9kRx7GcmAnCAXMYESsiVmYbpXQiOXYvEGr+q4fRK3Yexy5xXAKykSxam+4/448Z5USyiGA5yURRPKh/8vrr704c5/su5883MnIlHcXy6KMXefHFj7KwUB+7b78fjrRhHsqVdBvmra3Wrs+3Xq9MER6j68xyoeDn7iuOY7a3WwO5sby8zltvfTAS9ZGVIFtbTYJA6sIIgiAIWUSazBhaa7TWLC4uZtanC0t2Op3cFrTTojpEdgjCbLMfsZLuDLTXVKB0AVv5rpgtjB8PE8mye8ys1k5GrgznxaQzUBGtfaKolkS6pMWJSh7TypVR0XLgL084AIIg4t69de7dW586rlDwWVxs5EauXLgwz0c+coVPf/o5Go3q2H17vf5Apmxu7uC6DrVaJRMBMlqnxRKGEVtbzUGL21u37vPaa+9MTIHZ2NiRAqiCIAjCgSHSZMZot9u88sorrK2tDSSInMAIgrAXHlSsWKkiYuVsYFJ1+nsam04TSqcKxbGfyJUCcVwkikpoXWBYf2VYj8U83qhgkTosJ5F+P2BpaZWlpdWp40qlQm4hW7vuiSeuEoYRa2vbvPPOnUGr23Tdj7QE2dnpSMquIAiCcGyINJlBOp0Ovd4prLAjCMKxcxBipV6v4/smZN7WPRKxcjp5sDShbBSLESyFJDVoGMmSlyZkRMqoXIkkTeiE0e32uXXrPrdu3c/dXq+bmiI7O5O/ZwRBEAThpCDSRBAEQdgXIlaEByGbJrQ7RqyMpgi5SZHbYlL0tkgcl3PShMBEsUTSrlkQBEEQhIdCpIkgCIJw4OxVrKSlyjSxYhGxcnYYRpPsnipk0oS8sVQhI1YKg1Qh067ZHvqkU4VUSqhImpAgCPmYiDkFOElXMgdQSWRcev1wOQwLAARBGdDJ94xOIuTizLphBzO7/mhfnyAI+Yg0EQRBEI6FOI7p9XpT0w1HxYrv+1QqFarVKpVKZU9ixXb9Ek4vJk1or+2aGWvVbOqweJk6LHY5v10zmKiZ0XoskiYkCCcBKy7GZYaVHHbZSX3Gxz/rWdRIq/ZwsOw4YSI+Qhwnwnw/mO+Ectmko4Vhd1AHykhdM08X3waXOB4u533/jD6nofi1ssWKFzOZ55WVM/JdJQj7Q6SJIAiCcGJ5WLFSLpep1WoiVoQBSrHPOizjKUJx7AHDbkImmqU6pV2zbdEs7ZoFwWI+X9lIjaHksKIjLTkmkZYeYKSAlZn289bHcWwEmRUbdjktGuKUZIhTkiQdBbI/PK8GgO83931fK3eGcyN60st2Wxw7mFM7NyVkXNKpjmaMm0iZbLTd8Lsr/bc0DCVMzDAqJi1h0pEy+36ZgnDiEWkiCIIgzDQHKVZsfRUQsSJkC8/uBXPFeFSyeEn0Sok49tG6SBRV0drHnqQoZU+OdCp6xZ7s2ZShw3mNgjCNB0lHyZ6E2/e13RepddmoDTPvpQRjNIjasGIjLTVGJUc20uII/jhHwPBvdPD7Nv9X7piQyRM0VsgYGTOUMDZSxhTzTkfHDCXM8P9+NGpm+J0n6UrCSUekiSAIgnDqkYgV4SgwwiNmb2lCauTEw0axFBK5YiRLFBUBmyYE6ZOO7ElnnCp6K1EsZ40HSUfJiow8HiwdZTwyIxoRGqdLbMwq5v8kPPD/h2EE0aiISQua4W1JVxJmAZEmgiAIgsD+xYqd7yZWAMIwHExBEIhYER6wXXM2iiVdh8V2FZrUrtk8prRrPk7OSjqKcLYxEuZwxFiedDlZ6Uqj60QOnhZEmgiCIAjCHnkYsWI7A+WJlUqlMhApNnIliiLpDCQAo+2aJ7/3LOkrtcMUIduuuTCQK1FUTk4WYHh11pyYjMuVs9Gu+eHSUeJk/Hj7a0lHEYSHJ5uutLf29XshGx1z1OlKo6ls09KVRiNlDuxPkEKh1HCyz1kpJ3VbJY89HOM4DtVqMfkbnT5EmgiCIAjCAbIXsaKUyqQBXbhwgXK5TK/Xo1wuUyqVqFaruK47OCAZfQwrVtJzQQCbJrR7q2YYb9dsU4Xi2M90E4qiEloXUvVXYChaRrsIHX67ZklHEQThoDis6BgjFxyUctHazMHO08sOSnmpCBofc5puJythbPqSjZ6BYR02+zr04DvPrFOD9cO6WRqtzW3HGaYvKRUnF3Ai4lgTxzFam7FxHBPHZru9rXU8GAeaXq9Ev9+j39/b788sIdJEEARBEI4YrXVGrOjkTG5jYyMzTimF53n4vp+ZF4tFSqUS5XKZYrFIuVymUCjkChbIpgdZwaKnnz0KZ4T9tmsebdVsDt795MrqsKPQtHbNUeShVEQUeZKOIgjCrqQjH9LRDo4zGv2QHWO3TxuTh/19nDRmt+3AQDKMC4dhJGl6e3pd3mS3W4lh7mfFtyKO1WDZTE7mdhTZdekIRGcgY4zESc8Hr5bR9KSRv4Z9xSwsBECPOD59KcgiTQRBEAThhKK1JggCgmD3E1oAz/MycsUu2+gVK1iq1Sqe52G7BaW7BkVRNBbBIjVYBBhNE9qddO2AdB2WQmGeOPbwvKakowjCEWOFgeM4mdsPKyQsDysc8ranhUF62cqEvO2ThES+fMjeHp32u/104IxM7pTbLuAD5zCCRSJNBEEQBEE4odhokm63u+tYx3EmRrFYyWLThAqFwphgsQeGablil0/PQaPwMAxTdbIH0IVCB4AwbB7DsxKEw0cpheu6uK5LqVQaCAq7bZqQSEvsUaZt28v2ydEPekwo5EmGvGgIe/+DEg6jk3BcWJG9H7aS+em70CLSRBAEQRDOIHEc0+/395x7nCdYCoVCJk3Iipb0CQIMrxzmRbFIsVtBEE4ijuPgOM5AfljRPCnCIo2tbRUEAd1ulyiK2NzcnCgk8qIfDjoCQhCEB0ekiSAIgiAIu2IjSfaC7SA0KlrSUSzlcpl6vZ7bohkYnEiMRrIIgiDsFSs70uLDLu8W1RGG4UAsd7tdut0uQRAM1k1KZRyNtltYWADGa1YJgjA7iDQRBEEQBOFA2UsHIYstdjsqWHzfp1KpDERLsVik0WjsWuxWWjYLwunCRnekIz3sMmRTUkYlSBAE9Hqmm0d62d4eFR9Sx0kQhDxEmgiCIAiCcGyki912Op1dx7uum5sqlO4kJC2bBeHkkK7vkRf1MY04jgffDzbSwy73+/1c2SGpf4IgHDQiTQRBEARBmBnsSdF+olikZbMgPByTIj32Ut8jiqJBZEe73R4sWwkyKdJDPmeCIJwURJoIgiAIgnAqedCWzaOiZVSwSMtmYRaZVt8DyE1xscu2loed2yKndj5JfEg3LUEQTgMiTQRBEARBENh/sdu9tGy2dVmkZbNwEORFeqTFRx7p91pefY9er5dbzDS9LAiCcJYRaSIIgiAIgrBPDrJl8+hkWzaPChZp2Tz77KW+x6SOLra+R6/XG6S2pAubTkpxkaLIgiAID4dIE0EQBEEQhENGWjafHialuNgIEJjc0SUMw0GKiy1mmk53mVbYVCKQBEEQjgeRJoIgCIIgCCeI/bRsBnIFi7Rsns6o8EjfzvsbpcVHur5HOtLDprlMEx+CIAjC7CHSRBAEQRAEYYY5iy2bbZrLpKiPSSkuMCwQPBrlYaM/JqW4SH0PQRCEs4lIE0EQBEEQhDPCSWjZbOu02HSWSakuk1JctNZorQfSo9PpDJatBJkU6XHaI2gEQRCEg0ekiSAIgiAIgjDGfls2u66bmyo0Kljm5uYGES/pwqZWeFj5MU18SH0PQRAE4agQaSIIgiAIgiA8NHtNX1lYWABgY2PjsJ+SIAiCIDw0znE/AUEQBEEQBEEQBEEQhJOISBNBEARBEARBEARBEIQcRJoIgiAIgiAIgiAIgiDkINJEEARBEARBEARBEAQhB5EmgiAIgiAIgiAIgiAIOYg0EQRBEARBEARBEARByEGkiSAIgiAIgiAIgiAIQg4iTQRBEARBEARBEARBEHIQaSIIgiAIgiAIgiAIgpCDSBNBEARBEARBEARBEIQcRJoIgiAIgiAIgiAIgiDkcBzS5CeBt4C3gf8iZ3sR+NfJ9q8DH0rWfxH4FvBaMv9C6j7/Ptnnd5Lp4sE/bUEQBEEQBEEQBEEQzhLeET+eC/xTjAC5DbwCfBX4fmrMrwIbwJPALwG/AfwisAr8LLAEfBz4A+Bq6n6/DHzzcJ++IAiCIAiCIAiCIAhnhaOONHkZE0FyE+gDvwV8eWTMl4H/LVn+beDHAAV8GyNMAF4HypioFEEQBEEQBEEQBEEQhAPnqCNNrgK3UrdvA5+eMiYEtoDzmEgTy88DfwX0Uuv+FyACfgf4bwE97Ym4rsvCwsI+n/7xMz8/f9xPQRCOBHmvC2cJeb8LZwl5vwtnCXm/C2eF0/xen8VCsM9hUnb+s9S6XwZ+APhsMv2tCff9CiaF55uLi4uH+RwFQRAEQRAEQRAEQZhxjjrS5A7waOr2tWRd3pjbmOfXANZS438X+NvAOyP3AdgB/hUmDeg3cx7/nycTy8vLemNj40Ffx7Ezy89dEPaDvNeFs4S834WzhLzfhbOEvN+Fs8JpfK8fdaTJK8BTwIeBAqbQ61dHxnwV+JVk+ReAf4dJtZkH/g2m486fp8Z7gA0b8YGfAb53CM9dEARBEARBEARBEIQzhNJ6aumPw+CngP8e00nnXwD/GPhHmLSZrwIl4F8CnwDWMWLlJvAPgf8SuJHa108ALeBPMcLEBf4t8J9j6ptMYwV4/yBe0DGwSLbGiyCcVuS9Lpwl5P0unCXk/S6cJeT9LpwVZvm9/jhwIW/DcUgT4eH5JvDScT8JQTgC5L0unCXk/S6cJeT9Lpwl5P0unBVO5Xt9FgvBCoIgCIIgCIIgCIIgHDoiTQRBEARBEARBEP7/9u4n1L98juP481esUGaS6dcQm7FQCoUJCzY/fxbGhhUmlI0FZWGwGJFIomxEmWbkT/mbWciYRFYkkvGvxuLnzy/8Fj8xNaUmX4tzdH9d5zLX/c4953zP41G3e+7nexfvuq/vp9PrnnO+ABOUJuv0mbkHgHMi62yJvLMl8s6WyDtbcZBZ90wTAAAAgAmuNAEAAACYoDRZvsvVA9XPGp5GXHVjdX/Dxy/fX90wy2RwdndVV6tfXLd2Ur4vVJ+sflv9vHr++Y0Je3O5R7+nyzxrsq/9/Pbx9x8cj2GJnl59r/pV9cvqHeO6zHOILrefc5fVZl1psg4vr57b0cc33VF9t7pl/H7HTHPBWd1dvfLY2kn5ftW4dkv1tupT5zMi7N2j3dNlnjW5u7Pv5zdWd1Yvql44HvvHEEv0SPWu6tnVrdXbx2OZ51Cd9dxl1VlXmqzTbdU94/E91WtnnAXO4gfVtWNrJ+X7tupz1a76YfXk6uI5zAiPNZnnEOxjP39Fw38sr1V/HY+PFzGwBH+qfjoeP1T9uro5mWc7NpV1pcny7arvVD9paOuqbmrYrKv+PP4Mh+KkfN9c/eG63/vjuAZrcpo9XeZZu9NmW+ZZo2dWz6t+lMxzmPZx7rLqrD9u7gH4n15aXame2tDI/ebY67vxCw6RfHNo7OlslWxziJ5Yfa16Z/X3Y6/JPIdi8+curjRZvivj96vVNxruAftLR5doXxxfg0NxUr6vNDx47d+e1tH7A9biNHu6zLN2p822zLMmj28oTL5QfX1ck3kO0T7OXVaddaXJsj2hetJ1x5cankp/b0dPHL69+ub5jwaPmZPyfW/1poanct9a/a2jywJhDU67p8s8a3fabN/X8L64Yfy6NK7B0lyoPtvwLJOPX7cu8xyafZ27rDrrbs9Ztpsa2rwa/lZfrL5d/bj6cvXW6nfV62eZDs7uS9XLqqc03Nt4Z/WRpvP9rerVDR9h9nD15nOeFc7qtHu6zLMm+9jPr1UfbHhPVH2g/3y4LCzBS6o3dvQxrFXvTeY5PPs6d1l11i/sdgd9+xEAAADA/8XtOQAAAAATlCYAAAAAE5QmAAAAABOUJgAAAAATlCYAAAAAE5QmAMCWvL/aVfdNvPbV6vvnOQwAsGxKEwBgiy5VL5h7CABg2ZQmAMDWXKseqN439yAAwLIpTQCArdlVH6peUz1n5lkAgAVTmgAAW/SV6sFcbQIA/BdKEwBgi/5Zfbh6XfWsmWcBABZKaQIAbNXnq99X75l7EABgmZQmAMBWPVJ9tHpD9YyZZwEAFkhpAgBs2V3V1erdcw8CACyP0gQA2LJ/VB+r3lJdnHkWAGBhlCYAwNZ9unqoevHcgwAAy6I0AQC27uHqE3MPAQAsz4Xdbjf3DAAAAACL40oTAAAAgAlKEwAAAIAJShMAAACACUoTAAAAgAlKEwAAAIAJShMAAACACUoTAAAAgAlKEwAAAIAJShMAAACACf8CiZLx3kV2ao8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1332x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "dark"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "colors = ['lime', 'white', 'blue']\n",
    "methods = ['central bootstrap', 'percentile bootstrap', 'norm bootstrap']\n",
    "show_FPR(final_results, methods, colors)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "763cd6de-e63d-477c-ac8e-2aca96db3581",
   "metadata": {},
   "source": [
    "Мы получили несколько интересных выводов:\n",
    "1) На 5000 все доверительные интервалы получились корректными: FPR везде равен 5% с учетом шума.\n",
    "2) Удивительно, но центральный интервал сходится намного дольше, чем оставшиеся 2 вида интервалов. Поэтому, несмотря на то, что доказательная база у процентильного бутстрапа хуже, рекомендуют использовать именно его.\n",
    "    \n",
    "---- \n",
    "\n",
    "Давайте также посмотрим, насколько похожи доверительные интервалы на больших выборках:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "902ca869-790a-4432-b227-a978ed243776",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "central bootstrap interval: (3.32. 3.54)\n",
      "percentile bootstrap interval: (3.34. 3.56)\n",
      "norm bootstrap interval: (3.32. 3.56)\n"
     ]
    }
   ],
   "source": [
    "theta_func = lambda sample: numpy.percentile(sample, 50, axis=1) \n",
    "ex_sample = example_dist.rvs(5000)\n",
    "result = fast_bootstrap_ci(ex_sample, theta_func, alpha=0.05)\n",
    "\n",
    "for ci_type in result:\n",
    "    left, right = result[ci_type]\n",
    "    print(f\"{ci_type} interval: ({round(left, 2)}. {round(right, 2)})\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "deb80759-df58-4717-a4e1-28b386867255",
   "metadata": {},
   "source": [
    "Мы видим, что все они очень похожи и сильно не отличаются. А если взять больше выборку?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "370d6137-6a63-41f5-b8d3-97cd6c23c71b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "central bootstrap interval: (3.39. 3.48)\n",
      "percentile bootstrap interval: (3.4. 3.49)\n",
      "norm bootstrap interval: (3.4. 3.48)\n"
     ]
    }
   ],
   "source": [
    "ex_sample = example_dist.rvs(50000)\n",
    "result = fast_bootstrap_ci(ex_sample, theta_func, alpha=0.05)\n",
    "\n",
    "for ci_type in result:\n",
    "    left, right = result[ci_type]\n",
    "    print(f\"{ci_type} interval: ({round(left, 2)}. {round(right, 2)})\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c5a908b2-970b-4c0f-9829-8697496f5c12",
   "metadata": {},
   "source": [
    "Значения практически совпали! Отсюда можно также сделать вывод, что мощность всех 3 доверительных интервалов одинакова на больших выборках."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f86bfcf2-0e3b-45d9-a0d5-2a888dccc7b5",
   "metadata": {},
   "source": [
    "## T-test vs. Bootstrap\n",
    "\n",
    "Мы уже поняли, что с помощью бутстрапа мы можем оценивать любые характеристики распределения, в частности средние. Мы также знаем, что для построения доверительного интервала для мат. ожидания существует t-test. В данном параграфе давайте посмотрим, есть ли какие-то преимущества у бутстрапа относительно t-test?\n",
    "\n",
    "Мы ответим на 3 вопроса:\n",
    "- может ли помочь bootstrap, когда не работает t-test?\n",
    "- мощнее ли bootstrap, чем t-test?\n",
    "- насколько быстрее один критерий, чем другой?\n",
    "\n",
    "Давайте проведем тот же эксперимент, который мы провели ранее, сравнивая дов. интервалы, но со средним."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "e56d00f3-882f-4bf4-9cce-569108e3280b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def mc_ttest_checker(N, example_dist, theta, alpha=0.05, MC_size = 1000):\n",
    "    numpy.random.seed(42)\n",
    "    \n",
    "    bad_cnt = defaultdict(lambda: 0)\n",
    "    for i in range(MC_size):\n",
    "        ex_sample = example_dist.rvs(N)\n",
    "\n",
    "        ttest_pval = ttest_1samp(ex_sample, popmean=theta).pvalue\n",
    "        bad_cnt['ttest'] += (ttest_pval < alpha)\n",
    "    \n",
    "    return mc_result_dict_creator(bad_cnt, MC_size)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "f4a176ca-1023-4ca7-9c47-d183461d1036",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "2eab00acca3a420ea5e1a68e2caf135b",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/8 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N_to_check = [5, 10, 20, 50, 100, 200, 500, 1000]\n",
    "\n",
    "example_dist = stats.expon(scale=5)\n",
    "theta = example_dist.mean()\n",
    "theta_func = lambda sample: numpy.mean(sample, axis=1) \n",
    "\n",
    "boot_results = {}\n",
    "ttest_results = {}\n",
    "final_results = {}\n",
    "for N in tqdm(N_to_check):\n",
    "    boot_results = mc_bootstrap_checker(N, example_dist, theta, theta_func, alpha=0.05, MC_size = 1000)\n",
    "    ttest_results = mc_ttest_checker(N, example_dist, theta, alpha=0.05, MC_size = 1000)\n",
    "    final_results[N] = dict(boot_results, **ttest_results)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "44056aee-4d45-4969-8eee-02b3677a4788",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1332x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "dark"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "colors = ['lime', 'white', 'blue', 'yellow']\n",
    "methods = ['central bootstrap', 'percentile bootstrap', 'norm bootstrap', 'ttest']\n",
    "show_FPR(final_results, methods, colors)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "719cfe79-564b-46e6-aa7d-bdd0b71bc639",
   "metadata": {},
   "source": [
    " Мы видим, что бутстрап начинает работать тогда же, когда и t-test, а до этого момента у него ошибка сильно больше! \n",
    " \n",
    "Давайте посмотрим на ширину доверительного интервала у этих методов."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "e3ba1151-0ce1-4170-b1f6-2a190c389c3f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "central bootstrap interval: (1.51. 4.68), length=3.17\n",
      "percentile bootstrap interval: (1.77. 4.94), length=3.17\n",
      "norm bootstrap interval: (1.6. 4.85), length=3.25\n",
      "ttest interval: (1.42. 5.03), length=3.61\n"
     ]
    }
   ],
   "source": [
    "N = 20\n",
    "example_dist = stats.expon(scale=5)\n",
    "ex_sample = example_dist.rvs(N)\n",
    "theta = example_dist.mean()\n",
    "theta_func = lambda sample: numpy.mean(sample, axis=1) \n",
    "\n",
    "result = fast_bootstrap_ci(ex_sample, theta_func, alpha=0.05)\n",
    "result['ttest'] = t.interval(alpha=0.95, loc=numpy.mean(ex_sample), df=len(ex_sample)-1, scale=stats.sem(ex_sample, ddof=1))\n",
    "\n",
    "\n",
    "for method in result:\n",
    "    left, right = result[method]\n",
    "    print(f\"{method} interval: ({round(left, 2)}. {round(right, 2)}), length={round(right - left, 2)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "804688c1-0c1e-4c76-9f40-649832d04bdb",
   "metadata": {},
   "source": [
    "Мы видим, что бутстрап сильно заужает ширину дов. интервала. Поэтому мы и получаем большой FPR у бутстрапа при малых выборках.\n",
    "\n",
    "Это значит, что \n",
    " - Бутстрап не работает в тех случаях, когда не работает t-test. И FPR у него сильно больше.\n",
    " - Тогда же, когда начинает работать t-test, начинает работать бутстрап.\n",
    "\n",
    "То есть при оценке мат. ожидания выборки бутстрап не помогает в тех случаях, когда t-test не работает. Более того, он опасней в использовании в этих случаях.\n",
    "\n",
    "\n",
    "Но может быть мощность у него будет больше?\n",
    "\n",
    "Посмотрим на доверительные интервалы бутстрапа и t-test, когда мы знаем, что оба метода работают:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "31491a69-0fe3-4a6c-8ed6-10bb2486e0e3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "central bootstrap interval: (3.97. 5.37), length=1.39\n",
      "percentile bootstrap interval: (4.11. 5.5), length=1.39\n",
      "norm bootstrap interval: (4.04. 5.44), length=1.4\n",
      "ttest interval: (4.04. 5.43), length=1.39\n"
     ]
    }
   ],
   "source": [
    "N = 200\n",
    "alpha = 0.05 \n",
    "ex_sample = example_dist.rvs(N)\n",
    "result = fast_bootstrap_ci(ex_sample, theta_func, alpha=alpha)\n",
    "result['ttest'] = t.interval(alpha=1 - alpha, loc=numpy.mean(ex_sample), df=len(ex_sample)-1, scale=stats.sem(ex_sample, ddof=1))\n",
    "\n",
    "\n",
    "for method in result:\n",
    "    left, right = result[method]\n",
    "    print(f\"{method} interval: ({round(left, 2)}. {round(right, 2)}), length={round(right - left, 2)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "86eec035-bdfa-462b-98dd-301b96e19d11",
   "metadata": {},
   "source": [
    "Мы видим, что интервалы у бутстрапа и t-test практически идентичны, и это при выборке размера 200. А если взять большую выборку?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "37bb7242-f397-4f7a-b9bf-8798d917fa0d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "central bootstrap interval: (4.91. 5.11), length=0.2\n",
      "percentile bootstrap interval: (4.92. 5.12), length=0.2\n",
      "norm bootstrap interval: (4.91. 5.11), length=0.2\n",
      "ttest interval: (4.91. 5.11), length=0.2\n"
     ]
    }
   ],
   "source": [
    "N = 10000\n",
    "ex_sample = example_dist.rvs(N)\n",
    "result = fast_bootstrap_ci(ex_sample, theta_func, alpha=alpha)\n",
    "result['ttest'] = t.interval(alpha=1 - alpha, loc=numpy.mean(ex_sample), df=len(ex_sample)-1, scale=stats.sem(ex_sample, ddof=1))\n",
    "\n",
    "for method in result:\n",
    "    left, right = result[method]\n",
    "    print(f\"{method} interval: ({round(left, 2)}. {round(right, 2)}), length={round(right - left, 2)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "81500f54-c392-47ce-9cc6-a77efcf3adfa",
   "metadata": {},
   "source": [
    "Результаты практически идентичны. А это означает, что мощность бутстрап-критерия не будет отличаться от мощности t-test-критерия.\n",
    "\n",
    "**Поэтому, если вы видите, что бутстрап дает доверительный интервал уже, чем t-test, то этим данным нельзя верить!** Очень вероятно, что у бутстрапа в этот момент FPR больше, чем заявлен!\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2dc39c63-b4f9-4067-8e63-bd8d83addc88",
   "metadata": {},
   "source": [
    "И финальное: давайте сравним время работы 2 критериев:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "7d5e5241-c58c-4bea-a59e-c37f80cb1210",
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 100000\n",
    "ex_sample = example_dist.rvs(N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "1810fab3-2fe6-426a-ac9b-8935c6b39d9a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1.26 s, sys: 604 ms, total: 1.87 s\n",
      "Wall time: 1.87 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "_ = fast_bootstrap_ci(ex_sample, theta_func, alpha=alpha)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "db7233fb-12e7-4b1b-9064-d8c5048c5306",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1.82 ms, sys: 0 ns, total: 1.82 ms\n",
      "Wall time: 1.23 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "_ = t.interval(alpha=1 - alpha, loc=numpy.mean(ex_sample), df=len(ex_sample)-1, scale=stats.sem(ex_sample, ddof=1))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "acd42a8b-0777-4ec3-b308-bec9411a0df6",
   "metadata": {},
   "source": [
    "Мы видим, что на больших выборках разница по времени > 1000 раз! \n",
    "\n",
    "Почему так происходит? \n",
    "1. На одну бутстрап выборку тратится примерно O(N) времени. А на создание B выборок &mdash; `O(NB)` времени. Это и есть примерное время работы бутстрапа.\n",
    "2.У T-test же этой проблемы нет: ему надо посчитать только среднее за O(N), посчитать стандартное отклонение за O(N) и константы квантилей за O(1) времени. \n",
    "\n",
    "В итоге из-за этого бутстрап работает около `B` раз дольше времени, что мы и увидели на данных.\n",
    "\n",
    "\n",
    "------\n",
    "\n",
    "Поэтому, подводя итог сравнения t-test с bootstrap:\n",
    "- bootstrap нельзя использовать, когда не работает t-test. Его FPR будет больше, чем у t-test.\n",
    "- bootstrap не выигрывает по мощности у t-test. Они дают идентичные дов. интервалы, когда корректно работают.\n",
    "- он работает в тысячи раз дольше, чем t-test.\n",
    "\n",
    "----\n",
    "\n",
    "\n",
    "# Итог: рекомендации к использованию бутстрапа\n",
    "\n",
    "- Если вам нужно построить доверительный интервал для какой-то характеристики, то бутстрап ваш лучший друг. Он может помочь вам построить доверительный интервал для характеристики у одной выборки, так и оценить разностсть характеристик в AB-тесте, между тестом и контролем.\n",
    "- При этом надо помнить, что на малых выборках его опасно использовать. Поэтому по возможности, проверяйте на Монте-Карло, можно ли использовать этот критерий в вашей задаче или нет.\n",
    "- Также надо помнить, что бутстрап не пофиксит проблемы t-test: его опасно использовать тогда, когда t-test не работает. Вы ошибетесь с этим критерием сильнее.\n",
    "- Ну и главное: этот криетрий очень долго работает. Поэтому, если вам надо реализовать критерий, который должен проанализировать гигантское число AB-тестов, то бутстрап вам не поможет.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "894fb770-aacc-4192-a50b-769640211619",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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