{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Введение в анализ данных\n", "\n", "## Что такое среднее и как с ним правильно работать." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "ExecuteTime": { "end_time": "2021-03-06T12:51:48.836506Z", "start_time": "2021-03-06T12:51:48.082486Z" } }, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "from random import choices, shuffle\n", "import scipy.stats as sps\n", "import matplotlib.pyplot as plt\n", "\n", "import seaborn as sns\n", "sns.set(style='whitegrid', font_scale=1.3, palette='Set2')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1. Кошачий университет\n", "\n", "Пусть у нас есть 20 групп котиков-студентов.\n", "\n", "**Вопрос:** сколько котиков в среднем в группе?\n", "\n", "**Ответ деканата:** посчитать количество котиков в каждой группе и взять среднее арифметическое полученных чисел.\n", "\n", "Проведем эксперимент. Сгенерируем 20 групп, причем в каждой будет от 10 до 30 котиков. " ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "ExecuteTime": { "end_time": "2021-03-06T12:51:48.847433Z", "start_time": "2021-03-06T12:51:48.838315Z" } }, "outputs": [ { "data": { "text/plain": [ "array([11, 26, 18, 17, 11, 13, 12, 27, 13, 26, 19, 19, 17, 26, 26, 10, 16,\n", " 29, 17, 19])" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "groups_count = 20\n", "\n", "groups_size = sps.randint(low=10, high=30).rvs(size=groups_count)\n", "groups_size" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Ответ получить очень просто:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "ExecuteTime": { "end_time": "2021-03-06T12:51:48.973743Z", "start_time": "2021-03-06T12:51:48.967741Z" } }, "outputs": [ { "data": { "text/plain": [ "18.6" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "groups_size.mean()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Теперь предположим, что мы хотим провести эксперимент согласно тому, как учат в анализе данных:\n", "* возьмем случайную выборку котиков, \n", "* спросим у них, сколько котиков в их группе,\n", "* усредним полученные ответы.\n", "\n", "*Замечание.* Следующие операции с точки зрения кода можно сделать более эффективно, однако приведенный код повышает эффектность изложения материала.\n", "\n", "Для начала давайте создадим список всех студентов-котиков, каждому из которых присвоим номер группы." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "ExecuteTime": { "end_time": "2021-03-06T12:51:50.057491Z", "start_time": "2021-03-06T12:51:50.051055Z" } }, "outputs": [], "source": [ "students_group = []\n", "\n", "for i in range(groups_count):\n", " students_group += [i] * groups_size[i]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Возьмем 30 случайных котиков, спросим их и усредним ответы" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "ExecuteTime": { "end_time": "2021-03-06T12:51:50.779224Z", "start_time": "2021-03-06T12:51:50.772840Z" } }, "outputs": [ { "data": { "text/plain": [ "20.7" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "random_indexes = np.array(choices(students_group, k=30))\n", "groups_size[random_indexes].mean()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Хм, среднее получилось больше, чем ответ деканата. Может случайно так получилось? Ведь эксперимент случайный.\n", "\n", "Давайте повторим эксперимент 10 раз." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "ExecuteTime": { "end_time": "2021-03-06T12:51:54.372502Z", "start_time": "2021-03-06T12:51:54.350280Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "21.67\n", "21.0\n", "20.67\n", "19.37\n", "21.33\n", "19.3\n", "20.6\n", "22.43\n", "21.43\n", "21.3\n" ] } ], "source": [ "for _ in range(10):\n", " random_indexes = np.array(choices(students_group, k=30))\n", " print(np.round(groups_size[random_indexes].mean(), 2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Что-то все равно не так...\n", "\n", "А что будет если опросить вообще всех котиков? Навернято хоть тут должен получиться тот же ответ.\n", "\n", "Попробуем" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "ExecuteTime": { "end_time": "2021-03-06T12:51:56.705167Z", "start_time": "2021-03-06T12:51:56.699454Z" } }, "outputs": [ { "data": { "text/plain": [ "20.50537634408602" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "groups_size[np.array(students_group)].mean()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Хм, ответ все равно получился не тот, что сказали нам в деканате... В чем же дело?\n", "\n", "Оказывается, дело в том, что выбирая случайного котика мы чаще попадаем на котика из большей группы. В самом деле, если\n", "* $n$ — общее количество котиков, \n", "* $n_j$ — количество котиков в группе $j$,\n", "\n", "то вероятность того, что случайно выбранный котик учится в группе $j$ равна $n_j/n$.\n", "\n", "Посчитаем теперь средний ответ котика. Пусть $\\xi$ — количество студентов в группе у случайно выбранного котика. Тогда \n", "$$\\mathsf{E} \\xi = \\frac1n \\sum_{котик\\ i} \\sum_{j} n_j \\cdot I\\{котик\\ i\\ из\\ группы\\ j\\} = \\frac1n \\sum_{j} n_j^2.$$\n", "\n", "Проверим ответ:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "ExecuteTime": { "end_time": "2021-03-06T12:52:01.875384Z", "start_time": "2021-03-06T12:52:01.866131Z" } }, "outputs": [ { "data": { "text/plain": [ "20.50537634408602" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(groups_size**2).sum() / groups_size.sum()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Это среднее можно посчитать другим способом:\n", "$$\\mathsf{E} \\xi = \\sum_j n_j \\cdot \\mathsf{P}(случайный\\ котик\\ из\\ группы\\ j).$$\n", "\n", "Если рассматривать в качестве данных сами группы, а не котиков, то такой тип усреднения называется **взвешенным средним**. Общая формула взвешенного среднего чисел $x_1, ..., x_n$ с неотрицательными весами $w_1, ..., w_n$, для которых выполнено $\\sum_{i=1}^n w_i=1$, имеет вид $$\\sum_{i=1}^n w_i x_i.$$\n", "\n", "**Выводы:**\n", "* Деканат в качестве объектов данных рассматривает группы и берет по ним арифметическое среднее.\n", "* При проведении опроса объектами данных выступают котики, и арифметическое среднее по котикам отличается от результата деканата.\n", "* Деканат может взять взвешенное среднее и получить тот же ответ, что при проведении опроса.\n", "\n", "Этот пример — частный случай **парадокса инспекции**, который можно охарактеризовать как непосредственную зависимость наблюдения количества с самим наблюдаемым количеством." ] }, { "attachments": { "huff1.jpg": { "image/jpeg": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "### 2. Средняя зарплата\n", "\n", "**Вопрос:** какова средняя зарплата населения?\n", "\n", "Важно отличать разные \"виды средних\":\n", "* обычное **среднее арифметическое**,\n", "* **медиана** — значение, слева и справа от которого одинаковое количество элементов,\n", "* **мода** — самое частое значение.\n", "\n", "Разницу между ними наглядно показывает иллюстрация из книги *Huff D. How To Lie With Statistics. — New York: W.W. Norton & Company, 1954*.\n", "\n", "![huff1.jpg](attachment:huff1.jpg)\n", "\n", "Посмотрим на численном примере. Сгенерируем зарплату 10 000 человек в соответствии с некоторым распределением." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "ExecuteTime": { "end_time": "2021-03-06T12:52:18.375632Z", "start_time": "2021-03-06T12:52:18.367762Z" } }, "outputs": [], "source": [ "count = 10000\n", "salary = np.abs(sps.t(df=2, scale=100).rvs(size=count))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Посмотрим на *описательные статистики*. Как мы видим, среднее достаточно сильно отличается от медианы." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "ExecuteTime": { "end_time": "2021-03-06T12:52:19.545372Z", "start_time": "2021-03-06T12:52:19.518971Z" } }, "outputs": [ { "data": { "text/plain": [ "count 10000.000000\n", "mean 143.361444\n", "std 274.727742\n", "min 0.014972\n", "25% 35.979807\n", "50% 81.488075\n", "75% 162.664021\n", "max 8320.602082\n", "dtype: float64" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pd.Series(salary).describe()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Посмотрим на гистограмму распределения. Однако, в данном случае в выборке есть **выбросы** — сильно выделяющиеся по сравнению с остальными наблюдения. Видимо, выбросами у нас являются миллиардеры. В анализе данных существуют специальные методы для работы с выбросами, однако не редко их просто выбрасывают из анализа.\n", "\n", "Выбросы сильно влияют на вид гистограммы. В данном случае видна широкая часть графика справа, в которой скорее какая-то пустота. Для наглядности стоит рисовать гистограмму в логарифмическом масштабе, на которой явно видно имеющиеся выбросы." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "ExecuteTime": { "end_time": "2021-03-06T12:52:25.290254Z", "start_time": "2021-03-06T12:52:24.284179Z" } }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(20, 6))\n", "\n", "plt.subplot(121)\n", "plt.hist(salary, bins=50)\n", "plt.xlabel('Зарплата')\n", "plt.ylabel('Количество человек')\n", "plt.title('Простая гистограмма')\n", "\n", "plt.subplot(122)\n", "plt.hist(salary, bins=50, log=True)\n", "plt.xlabel('Зарплата')\n", "plt.ylabel('Количество человек')\n", "plt.title('Гистограмма в логарифмическом масштабе')\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Попробуем убрать несколько выбросов и посчитать среднее по оставшимся элементам. Как видим, среднее достаточно сильно уменьшилось, хотя мы выкинули около 10 человек." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "ExecuteTime": { "end_time": "2021-03-06T12:52:34.238172Z", "start_time": "2021-03-06T12:52:34.219851Z" } }, "outputs": [ { "data": { "text/plain": [ "137.01957408968383" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "salary[salary < 3300].mean()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Такой вид усреднения обычно называется **усеченное среднее**. Чаще усеченное среднее рассматривают для симметричных распределений, исключая одинаковое количество минимальных и максимальных значений." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3. Когда придет мой автобус? Или каково среднее время ожидания автобуса.\n", "\n", "Вы приходите на автобусную остановку. Согласно расписанию автобус ходит каждые 10 минут. Вы засекаете время, и получается, что автобусы обычно приходят через 9-11 минут.\n", "\n", "**Почему так не везет?**\n", "\n", "Казалось бы, если автобус ходит каждые 10 минут, то в среднем его нужно ждать 5 минут.\n", "Однако, не все так просто. В действительности автобусы приезжают не точно по расписанию, а случайным образом. Оказывается, справедливо следующее утверждение.\n", "\n", "**Если автобусы приходят с одинаковой интенсивностью в 10 минут и независимо друг от друга, то среднее время ожидания составляет 10 минут.**\n", "\n", "Это называют *парадоксом времени ожидания*. Далее мы попробуем экспериментально проверить это утверждение. Теоретическое доказательство этих фактов ожидает вас на 3 курсе.\n", "\n", "Для точности вычислений возьмем достаточно большую выборку — миллион автобусов, которые приходят *с интенсивностью* раз в 10 минут и сгенерируем интервалы прибытия между автобусами." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "ExecuteTime": { "end_time": "2021-03-06T12:52:59.909857Z", "start_time": "2021-03-06T12:52:59.722681Z" } }, "outputs": [], "source": [ "count = 1000000 # количество автобусов\n", "tau = 10 # средний интервал между автобусами\n", "\n", "bus_arrival_times = sps.uniform(scale=count*tau).rvs(size=count)\n", "bus_arrival_times = np.sort(bus_arrival_times)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Посмотрим на гистограмму интервалов прибытия автобусов, сравнивая ее с графиком плотность **равномерного распределения**." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "ExecuteTime": { "end_time": "2021-03-06T12:53:01.502269Z", "start_time": "2021-03-06T12:53:01.097111Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "grid = np.linspace(-10, count*tau+10, 1010)\n", "\n", "plt.figure(figsize=(8, 5))\n", "plt.hist(bus_arrival_times, bins=50, density=True, label='Данные')\n", "plt.plot(grid, sps.uniform(scale=count*tau).pdf(grid), lw=5, alpha=0.5, \n", " label='Плотность $U[0, max]$', color='#FF3300')\n", "plt.xlabel('Время прибытия автобуса')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Прежде чем перейти к ответу на наш исходный вопрос, посмотрим, сколько в среднем автобусов приезжает на остановку в течении часа?\n", "Поскольку у нам может не получится ровное количество часов, посчитаем для первых 100 000 часов." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "ExecuteTime": { "end_time": "2021-03-06T12:53:02.800105Z", "start_time": "2021-03-06T12:53:02.667529Z" } }, "outputs": [], "source": [ "hours_count = 100000 # количество часов\n", "\n", "# количество автобусов за каждый интервал длиной в 1 час\n", "hist = np.histogram(bus_arrival_times, bins=60*np.arange(hours_count))[0]\n", "# количество интервалов, за которые приехало одинаковое количество автобусов\n", "x, y = np.unique(hist, return_counts=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Посмотрим на гистограмму распределения количества автобусов за час и сравним его с графиком дискретной плотности **пуассоновского распределения** с параметром 6. Число 6 есть теоретически ожидаемое количество автобусов в час если их интенсивность движения есть в среднем 1 автобус за 10 минут." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "ExecuteTime": { "end_time": "2021-03-06T12:53:04.656595Z", "start_time": "2021-03-06T12:53:04.269023Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "grid = np.arange(25)\n", "\n", "plt.figure(figsize=(8, 5))\n", "plt.bar(x, y/y.sum(), label='Данные')\n", "plt.plot(grid, sps.poisson(mu=60/tau).pmf(grid), marker='o', ms=10, lw=5, alpha=0.5, \n", " label='Дискр.\\nплотность $Pois(60/\\\\tau)$', color='#FF3300')\n", "plt.xlabel('Количество автобусов в час')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Теперь рассмотрим средние длины интервалов между прибытиями автобусов. Посчитаем также средний интервал. Как видим, он составляет примерно 10 минут." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "ExecuteTime": { "end_time": "2021-03-06T12:53:05.850893Z", "start_time": "2021-03-06T12:53:05.841104Z" }, "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "9.999999740914484" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "intervals = np.diff(bus_arrival_times)\n", "intervals.mean()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Посмотрим на гистограмму длин интервалов между прибытиями автобусов и сравним ее с плотностью **экспоненциального распределения**." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "ExecuteTime": { "end_time": "2021-03-06T12:53:07.521815Z", "start_time": "2021-03-06T12:53:07.129054Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "grid = np.linspace(-1, 70, 1000)\n", "\n", "plt.figure(figsize=(8, 5))\n", "plt.hist(intervals, bins=50, density=True, label='Данные', range=(0, 70))\n", "plt.plot(grid, sps.expon(scale=tau).pdf(grid), lw=5, alpha=0.5, \n", " label='Плотность $Exp(\\\\tau)$', color='#FF3300')\n", "plt.xlabel('Время между прибытиями автобусов')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Проведем опрос миллиона пассажиров с целью выяснить, сколько времени они ждали автобус" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "ExecuteTime": { "end_time": "2021-03-06T12:53:08.866241Z", "start_time": "2021-03-06T12:53:08.339682Z" } }, "outputs": [ { "data": { "text/plain": [ "10.000317351938968" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "n_passengers = 1000000 # количество пассажиров\n", "\n", "# сгенерируем для каждого пассажира время его прибытия на остановку\n", "passenger_times = sps.uniform(scale=bus_arrival_times.max()).rvs(size=n_passengers)\n", "# найдем время прибытия следующего автобуса поиском по отсортированному массиву\n", "i = np.searchsorted(bus_arrival_times, passenger_times, side='right')\n", "# вычислим интервал ожидания\n", "wait_times = bus_arrival_times[i] - passenger_times\n", "\n", "wait_times.mean()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Посмотрим на гистограмму времени ожидания прибытия автобуса и сравним ее с плотностью **ТОГО ЖЕ САМОГО экспоненциального распределения**." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "ExecuteTime": { "end_time": "2021-03-06T12:53:09.903941Z", "start_time": "2021-03-06T12:53:09.481020Z" } }, "outputs": [ { "data": { "image/png": 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wKEpLmsQxiSriAjU1lOWkLbHfVl5n/+e5vkRkPFIzMd498ZNBj8lFqqghYGKvAUEE5Do4o9TMDGblF6YpzAceZAPahumJiCoxePBgJCYmapT/97//Rc+ePY0QETVWHIqvoVKxGLkOzpoV9zkcT0Q1M27cOJw8eRInT57E3r17jR0ONVJM7PpUcgsbr7MTUV0pKSmBjY0N3Nzc4ObmBmdn9ROH5ORkTJo0CSEhIejWrRuGDRuG3bt3q7V58803MWfOHLWyAwcOwNfXV/V++fLlGDx4sFqbjIwM+Pr64uzZswCUzxn39fVFRob2O3369++PtWvXqt7n5+dj3rx5CAkJQUBAAF555RWcPn262r8Dqhsciq+FLCdXtK9YmJLI6+xEVG0ymQzm5uY66wsLC9GrVy9MmjQJ1tbWOHHiBGbOnAlPT0/06tXLgJGqEwQB7733HiQSCZYvXw4XFxccOXIE77zzDn7++We1LxVkGEzstZDj6AJBJIKo/Fl9wUNeZyeianvw4AFsbGx01vv6+qolyddffx1//fUX9u/fb9TEfvbsWcTExODUqVOwtbUFAIwdOxZnzpzBli1bMHfuXKPF1lQxsdeI8my8RCJBjqMznHOy1KtTE5nYiajKcnNz8ejRI7i7u+tsU1RUhJUrV+LPP/9ERkYGFAoF5HK5xsS6n3/+Gfv27VO9Ly4u1tjX7du3ERAQoHov6Ljk+Mwzz0AkEsHe3h7dunVDeHg4mjdvrtYmNjYWMpkMoaGhauVyudyoXziaMib2Wsp0dtOe2Dv3ME5ARNTo3LhxAwDQtm1bnW0WLVqEP//8E+Hh4Wjbti2srKywePFiPHig/mTJwYMHY8qUKar3R48exX/+8x+1Ns2bN8f333+vep+Tk4MRI0ZoHHPjxo1wcnJCRkYGIiIiMH36dGzevFmtTWlpKRwdHbF161aN7S0tLSvpNdUXJnZ99Kz/nunijg634tQLeZ2diKrh1KlTcHJyQps2bXS2OX/+PJ5//nkMGTIEgDKhJiYmakyys7GxQatWrVTvXV01J/lKJBK1NtbWmg+2AgBvb2+4ubmhVatWGDlypMYXBADw8/NDTk4OSkpKKv1iQobDxF5LuQ7OKBGLIS4pt+LUo0IgOx1w8TBeYERNnKK0xOALxihKSyA1E+tv+A+5XI7Tp0/jv//9LwYPHoysrMejf9nZ2QCU194LCgrQpk0bHD58GAMGDIC1tTU2bNiA+/fvayT2uiSXyyGTyZCRkYGDBw9qnQjXu3dv9OzZE++//z6mTZuG9u3bIycnB3///TdatmyJgQMH1lt8pB0Tey2VisXIdnSBW1a6ekVKAhM7kRFVJ8Ea65gXLlzAu+++CwDYuXMndu7cqdFm8uTJmDRpEj755BPMnj0bo0ePho2NDV5++WUMHTpU66I2daV///4AAHt7ewQEBOCzzz7TaCMSibBmzRpERkbiiy++QEZGBhwdHdG1a1deYzcSJvYaECoMsWe6uGsm9tREoGtvA0ZFRI2Rt7c3/vjjD611BQUF+OKLLwAAzZo1U7surs2mTZs0yoYOHYqhQ4eq3k+ePBmTJ09Wa+Pm5obr16+r3vfs2VPtfUUV47WyssL06dMxffr0SuMjw+ACNXUgy9lNs/DeHaD8crNERBVIpVI4OTlV2sbW1lbnNXAibXjGro+eyXOA8vnsColUvVAuAzJSAY/m2jcioiYvMDAQP//8c6VtZs+ebaBoyFTwjL0OCGZmyNa2vGxq/V37IiIi0oaJvY5kuGhZWCIlwfCBEDVBuhZYIWqsavN3mom9BrT9urVeZ7+fDGhZ9YmI6o5UKkVRUZGxwyCqU0VFRZBKpfobasHEXkfybO0BqwrrPJcUA2nJxgmIqIlwd3dHSkoKCgsLeeZOjZ4gCCgsLERKSkqlSwxXhpPn9KnqfxQiEeDVBrgVq15+9xbgrXs1KSKqHXt7ewBAamoqFAqFkaOpW3K5vNInvpmKptDP6vRRKpXCw8ND9Xe7upjY61LzttoTe88w48RD1ETY29vX+D/BhiwqKgrdunUzdhj1rin005B9rNJQ/JEjRzBs2DD4+flh4MCB2LFjh95t5HI5IiIi0Lt3b3Tt2hVjxozBrVu31Nrk5ORg5syZCAkJQbdu3TBkyBCNBww0Ks19NMsy7wFFBYaPhYiImiS9if3SpUuYPHkyBg4ciD179mD06NGYM2cODh8+XOl2CxcuxL59+7BgwQJs27YN1tbWGDduHAoKHie5mTNnIiYmBt988w3279+Pt956C19++SV++eWX2vesPul4uIvC2hZw0jKJ7q7yC42itESzjoiIqA7pHYrfuHEjgoKCVEsQ+vj44NKlS1i3bh3CwrQPMefn52Pr1q344osv0LdvXwDKRw4GBwfjwIEDePXVVwEA0dHRmDRpEoKCggAAI0aMwNatW3H58mU8++yzddJBQ5KaiRGZm4Q2SfFq5Xd/f4CL958w+AMpiIio6dF7xn7hwgWEhISolYWGhiI2NlbnRJWYmBgoFAoEBwerymxtbREYGIjo6GhVWVBQEH7//XdkZmZCEAScOXMGiYmJ6NOnT037Uw+qN8s2w1XzwS9uWelVn4RHRERUC3rP2DMzM+Hi4qJW5ubmBoVCgZycHK3T8TMzMyESiTS2c3V1RUZGhur94sWLMX36dAQHB0MikUAkEuHzzz9H797Vf3hKbGys/kY14HDrFqzvpQIAvJp56W2f6eyKUjMzmJVbJ95C9gj2eQ8AKCdQNHSNIcbaYh9NA/toOppCPw3VR6POio+MjERycjK+++47uLu74++//8YXX3wBV1fXap+1+/n5wcLCou6DzEsGivOq3LxULEG2kytcKzztzS0zDQBUlx0aqqioqAYfY22xj6aBfTQdTaGfddlHmUxW6cms3sTu6uqKrKwstbLMzExIJBKdTyVydXWFIAjIyspSO6Mv/z4pKQkbN27Ejh074O/vDwDo2LEj4uLi8N133zWw4Xh1gva5cyoZLu6aib3iY12JiIjqgd5r7AEBATh16pRa2YkTJ+Dv769zubuyutOnT6vKCgoKEB0djcDAQABQLQEpFovVthWLxY1+9ah0N0+NMuecTEAhN0I0RETUlOhN7GPGjMH58+exYsUKJCQkYPPmzdi/fz8mTJiganPo0CEMHjwYaWnK4WZbW1uMGDECS5YswfHjxxEXF4fw8HA4ODhg6NChAJSz61u3bo3PPvsMUVFRSE5Oxvbt27F7924888wz9dTdGqjBl4w8W3vILCzVysxKS5XPaCciIqpHeofiu3XrhsjISCxbtgyrV6+Gp6cn5s2bp3arW15eHhITE9VmyU+fPh1isRjh4eEoLCxEQEAA1q9fDxsb5XrqEokE69atw9KlS/HBBx8gLy8PXl5emDp1KkaPHl0PXTUgkQgZLu5onpqkXn73FtCyvXFiIiKiJqFKk+fCwsJ03rMOAMOHD8fw4cPVyszNzTFz5kzMnDlT53YtWrTA119/XcVQG5d0Vw/NxJ4cr70xERFRHeHT3WpEz+w5AJnans+emwnk5dZ9OERERP9gYq8ncgtLPLDXctfAnRuGD4aIiJoMJnZ9ajFDP81NcxU6JDGxExFR/WFir0fpbs00C1Nv87Y3IiKqN0zs9SjXwUnjtjeUFAMpicYJiIiITB4Tew0IOh7bqkEkQrqWh8JwOJ6IiOoLE7s+tVwFT9sqdEi6yae9ERFRvWBir2cZrh4oNavway54CGSlGScgIiIyaUzs9axYIkW2k6tmBYfjiYioHjCxG4DO4XgiIqI6xsReA9W9Op6mLbGn3wWKCuokHiIiojJM7PrUwSS3Ahs7FFjbau6Xa8cTEVEdY2I3EO3D8bzOTkREdYuJ3UDStK1Cl3QTKC42fDBERGSymNgNJMvZFai4Cp1CDqRyFToiIqo7TOw1UdWV58oRzMyAFu01K27H1UFARERESkzsetXhCnFtOmmW3bkOlJbW3TGIiKhJY2I3IIVXa0AsUS8szAfSU5T1pSWGD4qIiEyKRH8TqitSS2usy78Hj4z7auW39q/CNV9/rAl9zUiRERGRqeAZu4Hdd/fSKPNMS+FDYYiIqE4wsdeAgOpPniuT5q5525tNYQHs8h/WJiQiIiIATOz61fGZtNzCEtlOLhrlnumpdXocIiJqmpjYjUD7cPw9I0RCRESmhondCLQldoeHOUD+AyNEQ0REpoSJ3QgKbWzx0M5BsyLxmuGDISIik8LEXhM1nzuncl/LJDokXK39jomIqEljYtennm5Du+fZXLPwfhLA2fFERFQLTOxGkmdrj3wbO82KRJ61ExFRzTGxG4tIhFRPb83yW1cMHwsREZkMJnYj0jocn5bM2fFERFRjTOw1INTgsa3a5Nk5IN9Wy3A8J9EREVENMbHrU89ruKdqO2tP4HA8ERHVDBO7kd3z0HKdPe0uh+OJiKhGmNiNjMPxRERUl5jYGwAOxxMRUV1hYq+B2jy2VRutiT3tLvAwp06PQ0REpo+JXZ96njwHAPm29siztdesiI+p92MTEZFpYWJvIFKatdAsvHnZIF8siIjIdDCxNxApXloSe24mkMnntBMRUdUxsTcQRVY2QLNWmhUcjiciompgYq+Jup0791j7rppl8TFAaWk9HZCIiExNlRL7kSNHMGzYMPj5+WHgwIHYsWOH3m3kcjkiIiLQu3dvdO3aFWPGjMGtW7c02l25cgUTJkxAYGAgunfvjuHDhyMxMbH6Pak3hrvGrWjlC4jF6oWF+UCq8vehKC0xWCxERNQ4SfQ1uHTpEiZPnoyJEydiyJAhOHPmDObMmQNHR0eEhYXp3G7hwoX45ZdfsGDBAnh4eCAyMhLjxo3DwYMHYWNjAwCIiYnB6NGjMWLECHz00UewtbVFQkICrK2t666HjYjU2hbfFaTDMz1VrTx570pc8u+BNaGvGSkyIiJqLPQm9o0bNyIoKAiTJ08GAPj4+ODSpUtYt26dzsSen5+PrVu34osvvkDfvn0BAIsWLUJwcDAOHDiAV199FQDw5Zdfon///pgxY4Zq25YtW9a6U41ZilcLjcTudT8FMZ27GycgIiJqVPQOxV+4cAEhISFqZaGhoYiNjYVCodC6TUxMDBQKBYKDg1Vltra2CAwMRHR0NAAgKysLFy5cQLt27TB+/Hj06tULL730Eg4ePFib/jR6aW7NUCxR/74lLimGZzpnxxMRkX56z9gzMzPh4uKiVubm5gaFQoGcnBy4u7tr3UYkEmls5+rqioyMDABAcnIyAGDNmjX44IMP8PHHH+PMmTP497//DWtra/Tr169aHYmNja1W+6pySkyEZZryDNqrmReAul95rrxSsRj3PLzRIuWOWnnz1CQAQFRUVL0du4whjmFs7KNpYB9NR1Pop6H6qDex1xfhn4VXBgwYgLFjxwIAOnXqhEuXLuHHH3+sdmL38/ODhYVFXYcJpMcBZtpHJurLXa+WGondPeM+UJCHoKCgej12VFRUvR/D2NhH08A+mo6m0M+67KNMJqv0ZFbvULyrqyuysrLUyjIzMyGRSODk5KRzG0EQNLbLysqCm5sbAKh++vj4qLXx8fHBvXtNe9g5y9kNRZZaJhDevGT4YIiIqFHRm9gDAgJw6tQptbITJ07A398fUqlU6zZldadPn1aVFRQUIDo6GoGBgQAAb29veHp6atzadvv2bXh7a3lGeVMiEiHZW8skwrgLXGKWiIgqpTexjxkzBufPn8eKFSuQkJCAzZs3Y//+/ZgwYYKqzaFDhzB48GCkpaUBUE6UGzFiBJYsWYLjx48jLi4O4eHhcHBwwNChQwEAIpEIb7/9Ng4ePIitW7fizp072LJlC3777Te88cYb9dTdxuOud2vNwgdZyqe+ERER6aD3Gnu3bt0QGRmJZcuWYfXq1fD09MS8efPUbnXLy8tDYmKi2iz56dOnQywWIzw8HIWFhQgICMD69etV97ADwBtvvAGFQoE1a9bgyy+/RJs2bbBkyRL06dOnjrtZx0T1N3muTKG1DbKcXeGSnalecf0C4KllXXkiIiJUcfJcWFhYpYvRDB8+HMOHD1crMzc3x8yZMzFz5sxK9z127FjV5LkGyYhD38nerTUT+61Y4KnBgNTcOEEREVGDxrXiG7B7Ht4a97RDIQcSrxknICIiavCY2BuwEokEqZ7NNSuuXzB8MERE1CgwsTdwydom0aXeBh5kGzoUIiJqBJjYa8CQV91zHJ2Rb2OnWREXbcAoiIiosWBi18fY942LREj2bqVZfv0CUMLHuBIRkTom9kYg2bsVSs0qfFRFBcDtOOMEREREDRYTeyMgt7DEfXcvzYpr5w0fDBERNWhM7I3EnZZtNQtTEoHcTM1yIiJqspjYa0AwwMpzFWU5uQKOrpoV10z/UYdERFR1TOz6GHvyXBmRCOjcQ7P8+kWg2LCPlSUiooaLib0RUfj4AeIKK9HJioCEq8r6Us6SJyJq6qq0Vjw1DFJrW6ySZ6NFyh218pw9qTjVqx/WhL5mpMiIiKih4Bl7I3OnRRuNMqfcLDg8yDFCNERE1NAwsdeI4SfPlcl1cMZDOweN8jZ34o0QDRERNTRM7Ho1kMlzZUQiJLb00Sj2un8XKMw3QkBERNSQMLE3QileLSCv8Dx2s9JS3vpGRERM7I1RqViCJC3X2nH1HNePJyJq4pjYG6nbLdtqLpRTmA8kXDFOQERE1CAwsdeAYLy5cyqPLK1xz8NbsyL2bMNZVIeIiAyOiV2fBpwkE1u10yxMTwHS7ho+GCIiahCY2BuxHEdnPLB30qyIOWP4YIiIqEFgYm/MRCIkttK89Q2J14AH2YaPh4iIjI6JvZFLadYCjyws1QsFAbh82jgBERGRUTGx14QRHtuqi2Bmpv1a+/WLXLCGiKgJYmLXpwFPnitzp0UbFEsqPM+npBi48rdxAiIiIqNhYjcBxVJz3GnRVrPiyjlAITd8QEREZDRM7CYioVU7QCxWL5QVAXHRxgmIiIiMgondRMgsrYB2XTUrLp/hMrNERE0IE3sNNNSr7gr/npqF+Q+A+BhlfSkTPBGRqZPob9LENYLJc2WkLp5Y9ygTHun31MoLdiTiaMgzWN33DSNFRkREhsIzdhNzs62vRplNYb7yee1ERGTymNhNTK6jCzJc3DXK2yfEAaWlRoiIiIgMiYndBN1o10mjzDY/T7nULBERmTQm9hrQeA56A5Pj5IosZ1fNiuhjjWrOABERVR8Tuz6NNBHe8NE8a0d2OnA7zvDBEBGRwTCxm6gsZzdkO7loVkTxrJ2IyJQxsZsqkUj7WXvWfeDWFcPHQ0REBsHEbsIyXdyR4+isWXH+T86QJyIyUUzsNdKwJ8+piESIa99Fs/xBFnDjosHDISKi+sfErlfjvh6d5eKOTC33tSPqGFBcbPiAiIioXjGxNwFx7TtrFuY/AK6dN3wwRERUr6qU2I8cOYJhw4bBz88PAwcOxI4dO/RuI5fLERERgd69e6Nr164YM2YMbt26pbP9J598Al9fX6xdu7bq0VOV5Dq64L67l2bFhRN8XjsRkYnRm9gvXbqEyZMnY+DAgdizZw9Gjx6NOXPm4PDhw5Vut3DhQuzbtw8LFizAtm3bYG1tjXHjxqGgoECj7d69exEXFwd3dy1DxlQnrrfvDFRcWKeoQPlYVyIiMhl6E/vGjRsRFBSEyZMnw8fHB2+88QaGDh2KdevW6dwmPz8fW7duxbRp09C3b1907NgRixYtQm5uLg4cOKDW9vbt21i0aBG++uorSKXS2vfIAIRGMneuvDw7B6Cdv2bFpVNAQZ7hAyIionqhN7FfuHABISEhamWhoaGIjY2FQqHQuk1MTAwUCgWCg4NVZba2tggMDER0dLSqTC6XY+rUqfjggw/Qtm3bmvahfpnQYi6KgFDArMJHrpArb38Dn9dORGQK9D6PPTMzEy4u6iuYubm5QaFQICcnR+vweWZmJkQikcZ2rq6uyMjIUL1ftGgRWrZsiVdeeaWm8avExsbWeh/auN65A2luOgDAq5mW69SNiNTJDZFCAdokxatXJMXgWEEKlgyZCACIiooyQnSGxT6aBvbRdDSFfhqqj3oTe335448/cOTIEezZs6dO9ufn5wcLC4s62ZeapGjAymi/pjp3w6cjmqfcgbRYfbSlc9xlYIjyz0FBQUaIzHCioqLYRxPAPpqOptDPuuyjTCar9GRW71C8q6srsrKy1MoyMzMhkUjg5OSkcxtBEDS2y8rKgpubGwDgzJkzuHfvHnr16oXOnTujc+fOSElJwddff40ePXro7RjVjMLcAjd9OmqUu2WlA8nxWrYgIqLGRG9iDwgIwKlTp9TKTpw4AX9/f52T3crqTp8+rSorKChAdHQ0AgMDAQDvvPMO9u7di927d6te7u7uePPNN7F169ba9MkAGuHsuXJut/RBoZWNZsVfv3OpWSKiRk5vYh8zZgzOnz+PFStWICEhAZs3b8b+/fsxYcIEVZtDhw5h8ODBSEtLA6CcKDdixAgsWbIEx48fR1xcHMLDw+Hg4IChQ4cCUF6n79Chg9pLKpXC1dUVPj4+9dTdGjChyXNlSsViXOvgp1mRnQ7rO1cNHxAREdUZvRePu3XrhsjISCxbtgyrV6+Gp6cn5s2bh7CwMFWbvLw8JCYmqs2Snz59OsRiMcLDw1FYWIiAgACsX78eNjZazhTJ4O55eiPnjgucctUvl9hdPw8UvgRY2xopMiIiqo0qzQoLCwtTS+QVDR8+HMOHD1crMzc3x8yZMzFz5swqB/PHH39UuS3VkkiEKx27IuSvP9WKzRQy4O/DQL8XjBMXERHVCteKrwGh4gpujVSuozOSmrfWrLh+EbifbOhwiIioDjCxN3Fx7btAIdEyCfLUQU6kIyJqhJjY9THByXPlyS0sEddByzPbM+8B10x/wQgiIlPDxE5Iat4GD+0cNCvO/aF8UAwRETUaTOwEwcwMMZ0DNCtkRcCpXwwfEBER1ZjprJVqQKY4OJ/j5IJiW29orIZ/KxZo3xVo1QGK0hJIzcTGCI+IiKqIiZ1UJL0HYefx7ZAq5Grlj/77OY6GPIOVT79lpMiIiKiqOBSvj4lPnlNjZYMrHbtqFFs+KkLHG1eMEBAREVUXEzupuevVEhkumo/ibZ10i/e2ExE1AkzspE4kQkyXQJSItVxLP74XKC42fExERFRlTOw1YSIrz+lSaG2D6+213NuekwGc/1OznIiIGgwmdtIqsaUPHtg7aVZcPg3cTzJ8QEREVCVM7Ho1oclz5QhmZrjoH4RSswp/RQQB+HMXIJcZJzAiIqoUEzvplGfngBs+nTQrHuYAf/1u+ICIiEgvJnaq1K02HZDj6KJZcS0KuHPD8AEREVGlmNhrwFQe21oVZUPyOmfJcy15IqIGhYmd9CqwscNVX3/NisJ84OjuprWIDxFRA8fErg+TFgDgTou2QIt2mhVJN4HLZwwfEBERacXETlUjEkER+n+ApbVm3d+HgbS7UJSWGD4uIiJSw4fAUJVJ7Rzxqa0YT96I0agr+u4TvDrtO8CCT38jIjImnrFTtaS7N0NC6/Ya5VZFhcrJdLx0QURkVEzsVG3XOvhpX5Uu4SoQe9bwARERkQoTuz48A9UgmJkhqntPFEu0XMn563cg9bbBYyIiIiUmdqqRQmsbXOoSpFlRWgoc3g7kPzB8UERExMRONXevWXMktvLRrCgqAA5t4yNeiYiMgIm9BprSynP6XPXtimwnV82K9BTg1EFeyiAiMjAmdqqVsuvtjywsNSvjooErfxs+KCKiJoyJXR+eceols7DE+YBegLb15E//yofFEBEZEBM71YlcRxcoeg/SrBAE4MgOIPM+V6YjIjIArjxHdUba5UksP7EdrZMTNOoefXsVr3z0LWBjZ4TIiIiaDp6x14AATp7T5Uqnbshwcdcot3xUBPz2P0AhN0JURERNBxM71amyyXR5tvaalRmpytvgSjgkT0RUX5jY9eHkuWorlprj76CnIDe30KxMjucz3ImI6hETO9WLIisb/B3YG6VmWv6KxccoZ8szuRMR1Tkmdqo3uY4uiO72pPbK2LPAxZOGDYiIqAlgYq8Jzp2rsvse3rjUJVB75d9HgFguYENEVJd4uxvVu+QWbWAhl2GYTEvlqYOAmRnQuYfB4yIiMkU8Y9eL14HrQnxbXxT76RiWP7EfiIvmAjZERHWAZ+xkGCIRJE89i28vHkLz1CTN+k0xGDb6U8C3u8FDIyIyJTxjJ8MRiXDJLwipns211x/bA8RdMGxMREQmhom9BrjyXM0JZma40PUJ3PPw1lIpKJN7zF+GD4yIyERUKbEfOXIEw4YNg5+fHwYOHIgdO3bo3UYulyMiIgK9e/dG165dMWbMGNy6dUtV//DhQ8yfPx/PPvssunXrhtDQUEybNg337t2reW+oURDMzBDd7Unc9/DS3uD0r0D0cd7nTkRUA3oT+6VLlzB58mQMHDgQe/bswejRozFnzhwcPny40u0WLlyIffv2YcGCBdi2bRusra0xbtw4FBQUAAAyMjKQmpqKf//739izZw8iIyNx584dvP322yhpSEuOMrnUC8HMDFHdeiLNvZn2Buf+AM4e4u+fiKia9Cb2jRs3IigoCJMnT4aPjw/eeOMNDB06FOvWrdO5TX5+PrZu3Ypp06ahb9++6NixIxYtWoTc3FwcOHAAAODj44NVq1YhLCwMrVu3RkBAAD7//HPcvHkT8fHxdddDarAEMzOc795L9zX3S6eB4/uA0lLDBkZE1IjpTewXLlxASEiIWlloaChiY2OhUCi0bhMTEwOFQoHg4GBVma2tLQIDAxEdHa3zWHl5eQAABweHKgVPjV/ZNfek5q1RImhJ4HHRyqfCyWW8HY6IqAr03u6WmZkJFxcXtTI3NzcoFArk5OTA3V3zEZ2ZmZkQiUQa27m6uiIjI0PrcWQyGSIiItC/f394enpWpw8AgNjY2GpvUxXuyckQFz4EAHg1++easIiT5+qSYGaGy10CIZa4YN+B7zQbJMXgweU/8MakZYiKu1Enx4yKiqqT/TRk7KNpaAp9BJpGPw3VxwZxH7tcLseUKVNQXFyMBQsW1Ggffn5+sLDQ8jSx2rpxEniYU/f7JXUiEdB7EG5cP4kO8dc0qh0e5gK71yHo2dcBZ80vk9URFRWFoKCgWu2joWMfTUNT6CPQNPpZl32UyWSVnszqHYp3dXVFVlaWWllmZiYkEgmcnJx0biMIgsZ2WVlZcHNzUyt79OgRJk6ciLS0NPzwww8Nbxiek7cMRyTCjXadEdupu/b6/AfAnu+BpJsGDYuIqDHRm9gDAgJw6tQptbITJ07A398fUqlU6zZldadPn1aVFRQUIDo6GoGBjx8IUlhYiHfeeQfZ2dnYuHGjzi8K1LTcbuWDc4G9USIWa1bKZcCvPymfDMcvXUREGvQm9jFjxuD8+fNYsWIFEhISsHnzZuzfvx8TJkxQtTl06BAGDx6MtLQ0AMqJciNGjMCSJUtw/PhxxMXFITw8HA4ODhg6dCgA5cz5cePGIS0tDUuWLIFCoUBGRgYyMjLw6NGjeuouNRZp7l4480QfyM21XF4RBODsYeDIz0Cx9gmcRERNld5r7N26dUNkZCSWLVuG1atXw9PTE/PmzUNYWJiqTV5eHhITE9VmyU+fPh1isRjh4eEoLCxEQEAA1q9fDxsbGwDAlStXcOGCcvnQIUOGqB0zIiICw4cPr5MO1geBc+cMItfRGSd7PY0no07BtiBPs8GtWCA3Exg0ErBzNHh8REQNUZUmz4WFhakl8oqGDx+ukYjNzc0xc+ZMzJw5U+s2PXv2xPXr16sRKjVFhdY2ONWzHwIvndXeIOs+8PNqoN8LQOuOBo2NiKgh4lrx+vA6rtEpzM3xd1Awirv20t5A9gj4bQuKTx0AGtKqhURERtAgbncj0kcwM4Ok92DMS7qI7rFRMNOyGt0wAEhPBQa8DNhzIiYRNU08Y6dGJdWrJU727IciS2vtDdJTlEPz1y9ytIWImiQm9hrgY1uN66GDE44/NUD3A2TkMuDobuDQNqCowKCxEREZGxM7NUoKc3OcC+iNqx27otRMx1/jxGvA9lXAbU7SJKKmg4ldHw7nNlwiERJat8fpJ/uiyErH0HxRgfIhMkd3A48KDRoeEZExMLFTo5fr6IxjTw1AcTs/3Y2uX0TJ1uVAfAy/rBGRSeOseDIJxVJzSEJfxmfZCfC/cgHmCrlGm2Et/YEjP8O52Azo4MOZ80RkknjGXhOcO9dg3fNsjmPBYUhz0/3oX4uMu8pr7xdOAMXFBoyOiKj+MbGTyZFZWuFc4FO41CUQCon2BxWhWAH8fQTYvhK4HcfheSIyGUzsevE//EZJJEJyizY4GvIM7nl46273MAf4bQtw8EcgJ8Nw8RER1RMmdjJpMksrRAX0Uj4G1toWAODVzEuz4d1bKNm+EjixH9D2wBkiokaCk+eoSUhz94K450uI3DgHrZNuQaRl6H1YS3/g6nngxiXAryfQPQSwsDRCtERENccz9hrgynONlLkFrnTqhuNPDUCmi7vudsUK4OJJ4H/fKH/yme9E1IgwsVOTk2fngL96hOBcQG8UWtnobigrAs4eBn5aBlw8pVyqloiogeNQvD6cLW2aRCKkeXghw9UDbW/fRLvE6ygRSiEWafmuW1QAnD2EkgvHIe76FNDlScDSyvAxExFVARM7NWmlYjHifTriTos2eNHGG3sOfKf1kbDAP9fgz/8JXD4NdH5CmeBt7Q0cMRFR5ZjYiQAozC2AXgPxx8MkdLh1DS3v3tbdWC5TXnu/fBpo2wXw7wW4V3JLHRGRATGx14SIk+dM1SMra1z2C8Kt1h3QISEO3qlJuhuXlirXno+PATxbKhN8646ArqfNEREZABM7kRYFtna40PUJ3PDpiHYJ19G8sgQPAPeTlC8be6BjANAxELB1MEywRETlMLHrw8lzTVqBjR0u+ffAjXadMMTSA5Ibl4ES7evLlwilEBc8BKKOAdHHgRbtgE5BQMsOPIsnIoNhYieqgiIrG0hCn8MUeSZaJSegdVICzCvc/jaspf/jN4IAJN1UvmzsgHb+QLuugIsHL+UQUb1iYieqBpmFJW6064z4Nr7wvpeMNnfiYZ/3AAB03y5XkAdcOo2SiychdvEE2ndVJnoO1RNRPWBirwEOzlOpWIzk5q2R7N0KLtkZaJN0C2KxBPtuX9K5zbCW/kB2unLRm7OHgWatlLPqW3fkbXNEVGeY2IlqQyRClos7slzc8XbgMMRtX4xWdxNhVVSof9t7d5SvUwcBj+ZA605Am06Ag3P9x01EJouJXR9OnqOqsrFDvE9HxLf1hWtWOlonJ8A9477OBW/UpN1Vvs4eAlw8gda+QIv2gJsXJ94RUbUwsRPVNZEIma4eyHT1gFQug9f9FHjfS9J9Df4fqvqs+8pX1DHA0hpo7gO0bK/8Wdna9kREYGInqlcKcwvcadkWd1q2xVvdnsWSnUvRPCUJNoX5Gm3VZtWXeVT4eBEckUh5Bu/dFvBqrVwURyKt/04QUaPCxF4DAm9Xopqwd8JNn0642bYj7PMewDMtBV5pKbDNzwNQyaz6f5SUlkCcngKkpwAXTgBiMeDmrUzyXm2U1+mZ6ImaPCZ2IkMTifDQ3hEP7R1xo30X2OTnoVlaCobZN8e+qN90bqZxRl9S8njFu+jjgFiiPKP3aA7LzIdAQQflPfRE1KQwsevDyXNUzwps7RBv2xEIfQ1HbEVwz7gP98w0uGalQ1xSUvUdlRSrEr3TvVQgJRawcwTcmyvP5j1aAM4egIT/7IlMGf+FEzUgRVY2uNPSB3da+sCspATOOZnwyLgPt8y0qk++Ky8vV/m6Fat8b2YGOLkBrs0ev5w9AHOLeusTERkWEztRA1UqFqtm1wPAqG7PYv7+VXDNyYRLdgYsHxWptR/Soovqz17NvDT2VyKUQlwKICtN+bp+UVkhEgH2zv8keXfly9ENsHfirXZEjRATe41w8hwZgb0Tklu0QXKLNoAgwKYwHy7ZyiTvmp0BscgM+5JidG6uddY9oLzc9CBL+bpVrlwsARxdlWf4Tm7/JHxXwM5JOXGPiBokJnaixkgkQoGNHQps7JD0T6J/uduzuPDrWjjlZMHpQTbs8x5AVG6OSLWH8kuKH99TX56ZmXKde3tnwMFFuVKevbPyJ5M+kdExsevFyXPUCIhEgIMzUrxaIsWrJQBAXFwMx4c5qkQvtnXAvmunde6i/FC+NqrEX1oKPMxRvu7eUm8kEikn7Nk6PP5pW+69jT0n7xHVM/4LIzJRJRIJspzdkOXsBgCYEPoafj/sBIeHuXB4mAv7vAdweJgDm8ICAKj5UH55gvA46etiY/dPwndQJnprO8DaVvnTxk75U2rOx9sS1RATO1ETIrewRIabJzLcPFVlEoUc9nkPMMynN+4I+bDLz4Nd/kNIFXK1bWs0K1+bgjzlK+2u7jZSc82Eb2WjXGLXUvlTnJ8LyB4pZ/TzSwCRChN7DQj8P4RMSLHUHNnOboDfk4jJiVcWCgIs5DLY5j+E3T8vsVcb7Lh4GBayR1r3U+Wh/KpQyB9P6NPB/V4qEPfPCnyW1mpJH1Y2gIUVYGEJmFtq/7NEyi8EZJKY2IlIk0gEmYUlZBaWyHJxV5aFvoZDThaQFCtgXVgAm4J82BSWvQogtrHHvrgzOndZp4lfbcOSx6MA1SEWKxO9uaUy0VtY/fPeQjliIDUHpP/82dwCkJiXqytfzi8I1LAwsevDleeI1BRLpKolcct7K/Q1/PLnf2FdVACrokJYPSqEdVGh6s91NnnvHxXv1a/2F4OSEqCoQPmqDZHo8RcBibky0Usk//ys8BLrKK9YJ5YAYjHEhf98YfnnPczEyrsS+EWCKsHETkR1pkQiQZ6dA/LsHDTqRoe+hoNH3WH5qAhWj5TJ3vLRI1jIH8Hy0SOIPVthW+xRWMgeaX2G/bCW/pVO7qvtiECNRwwEAZDLlK865n4vFbh6VL1QJFImeIlE+bN80i/7s1ii5b1ZuS8GZspykZn292XtarKNSKQsE4n+idUMgKhcXYV6kRlQWqL8PfILS52oUmI/cuQIli1bhsTERHh5eeGdd97Byy+/XOk2crkcX331Ffbu3YuCggIEBgbi008/hY+Pj6qNIAhYvXo1tmzZguzsbHTs2BEzZ85EQEBA7XpVU8XFQFoyUFhuSK86a3UTUaVKxWIU2tii0MZWszL0NRxxsQIEAVKFHJayR7CQPYKlrAgWMhmGdeiNu8UPYCGXwVwuh7lcBnOFTLWeflVm9TfILwbVJQjKNQZKiuv/WAbS7F4qEH1Q+aaqXwZE5erV2po93k/ZFwXVnyu8L18PLe1VXzS0tK/O/sRiWGU+ALp3N8g6D3oT+6VLlzB58mRMnDgRQ4YMwZkzZzBnzhw4OjoiLCxM53YLFy7EL7/8ggULFsDDwwORkZEYN24cDh48CBsbGwDAhg0bsHbtWsyfPx++vr744YcfMH78eBw8eBCenp46910vigqA/T8A2en62/JbJVH9EYmgMLeAwtxC/cy/9yBcLNacTCcuLoa5QoZh3Yfg75NblQlfLoO0WAGpQgGpQg5psQLwaIH8rNv/lMs1RgUa4heD8pcbDPbFwdgE4fEJlQmdVzneSwXsLIABL9X7sfQm9o0bNyIoKAiTJ08GAPj4+ODSpUtYt26dzsSen5+PrVu34osvvkDfvn0BAIsWLUJwcDAOHDiAV199FYIgYP369Rg/fjyGDh0KAPj8889x8uRJ/O9//8PUqVOr1AHhn2vgcrlcT0s94i4C+XmAuVWlzcTWDrAVSVEs0vzVyWQy2GopZz3rWV+P9VIJILWEzMEVhe7NUahr+yeex3nXx4+xNSspgaS4GNJiBSTFCgzs1BdxFxwhLimBpFih/FlSDHFJCcQlxZC16ow8xUNIipXvJf+Ul31BKLawwW+p13XGP8DLt1b1/Zq1r9WIQUOuL7ayhUzP/72NXbGVLWRJ8cDDXOVEzVooy3eCjjlgIkFXzT/69euHUaNG4d1331WV7d27FzNnzsSFCxcglUo1tjlz5gzGjBmDEydOwN3dXVU+duxYeHh4YMGCBUhOTkZYWBi2bNmiNvQ+e/Zs3LlzB5s2bapSB/Py8nDjxo0qtSUiIjIVHTp0gJ2dnUa53jP2zMxMuLi4qJW5ublBoVAgJydHLXGX30YkEmls5+rqioyMDABQ/XR1ddVoc+7cOX1hqdjY2KBDhw6QSqUQcYiciIhMnCAIUCgUqsvaFTX6WfFmZmZav7EQERGZKktLS511emdiuLq6IitLfcJKZmYmJBIJnJycdG4jCILGdllZWXBzU65bXfYzMzNTo422UQAiIiLST29iDwgIwKlTp9TKTpw4AX9/f63X1wGo6k6ffrwYRUFBAaKjoxEYGAgAaN68Odzc3NT2LQgCTp06pWpDRERE1aM3sY8ZMwbnz5/HihUrkJCQgM2bN2P//v2YMGGCqs2hQ4cwePBgpKWlAQBsbW0xYsQILFmyBMePH0dcXBzCw8Ph4OCgmgEvEokwbtw4fP/99zh48CDi4+Mxd+5c5ObmYuTIkfXUXSIiItOm9xp7t27dEBkZiWXLlmH16tXw9PTEvHnz1G51y8vLQ2JiIhQKhaps+vTpEIvFCA8PR2FhIQICArB+/Xq1i/1jx46FTCbDggULVAvUrFu3Ds2aNavjbhIRETUNem93IyIiosajCSxjRERE1HQwsRMREZkQJnYiIiITwsRORERkQpjY9Thy5AiGDRsGPz8/DBw4EDt27DB2SLVy7tw5vPfeewgJCYGvry8OHDig0SY6OhqvvPIK/P390bdvX6xZs8YIkdbcd999h1deeQVBQUF48sknMWbMGFy4cEGjXWP+bLdu3Yrnn38eQUFBCAgIwPPPP49du3aptWnM/dNm9+7d8PX1xfjx49XKG3M/ly9fDl9fX41XcfHjR7I25v6VyczMxKxZs/DUU0+p+vHbb7+ptWns/ezfv7/Wz/Kdd95RtTFYHwXS6eLFi0KnTp2EyMhIIT4+Xti0aZPQqVMn4dChQ8YOrcaOHj0qLF26VPj999+FDh06CPv371erv3v3rtC9e3fh008/FW7evCns27dP6Nq1q7Bx40YjRVx9EyZMELZt2yZcu3ZNiI+PF2bMmCF0795duH37tqpNY/9s//jjD+HIkSPCrVu3hDt37ggbN24UOnXqJBw5ckQQhMbfv4pu3bolBAcHC6+//rowbtw4VXlj72dkZKTwzDPPCOnp6WqvMo29f4IgCHl5ecIzzzwjjB8/Xjh37pyQnJwsnDt3Trh8+bKqjSn0MysrS+0zvHLliuDr6yvs3LlTEATD9pGJvRIffvih8MYbb6iVffzxx8KIESOMFFHd0pbYFy9eLPTv318oLS1VlX399ddCaGioWlljUlJSIjz55JPCf//7X1WZKX62L7zwgrBgwQJBEEyrfzKZTHjuueeE3bt3C9OnT1dL7I29n5GRkcKgQYN01jf2/gmCICxdulTo37+/IJPJdLYxhX5WtGrVKiEoKEgoKioSBMGwfeRQfCUuXLiAkJAQtbLQ0FDExsaqLcZjSi5cuIDg4GC1J+WFhoYiLS0NKSkpRoys5mQyGeRyOezt7VVlpvTZlpaW4tSpU0hMTETPnj0BmFb/IiIi0KFDBzz//PMadabQz9TUVPTp0wdPP/00/vWvfyEuLk5VZwr9O3z4MAIDAzF//nwEBwdjyJAhWL58uVr8ptDP8gRBwI4dO/Dcc8+pHtZiyD4ysVdC3yNrTZGuPgOPH7Xb2CxatAj29vYYMGCAqswUPtvU1FQEBATA398fEydOxOzZs9GvXz8AptE/APj9999x8uRJzJ07V2t9Y+9n165dERERgbVr1yIiIgIlJSUYNWoU7ty5A6Dx9w8AkpKS8Ouvv0KhUGDNmjWYMmUKfvrpJyxdulTVxhT6Wd6pU6dw9+5dvPrqq6oyQ/ax0T+2lagyq1atwv79+7FhwwbY2toaO5w65e7ujt27d6OwsBCnT59GREQEPDw8EBoaauzQ6sS9e/cwd+5crF692uQ+uzJ9+/ZVex8UFIRhw4Zh06ZNmD17tpGiqluCIMDV1RXz58+HWCyGn58fsrKysHjxYoSHh6uNDpqKbdu2wd/fHx07djTK8ZnYK1GTR9Y2drr6DDw+c28sIiMjsWnTJqxfvx5+fn5qdabw2UokErRq1QoA0KlTJ9y9exfLly9HaGioSfTvypUryM7OxqhRo1RlpaWlAIDOnTtj27ZtJtHP8qRSKfz9/XH79m0ApvH31N3dHS1btoRYLFaV+fj4oKioCDk5OXB2djaJfpbJysrCH3/8gTlz5qiVG7KPHIqvRE0eWdvYBQQEqD1uF1D22cPDA97e3kaKqvoWL16MH3/8ERs2bIC/v79GvSl+tqWlpZDJZABMo3+9evXCvn37sHv3btWrf//+CAgIwO7du9G+fXuT6Gd5paWliIuLU32JNoX+BQQEICkpSfWlDABu374Na2trVUIzhX6W2blzJ6RSqepJpmUM2sc6n45nQspuT1i+fLlw69Yt4ccff2x0t2BUlJ+fL1y9elW4evWq0KFDB2HNmjXC1atXVbeCld3uNnfuXCE+Pl7Yv3+/0K1bN2HDhg3GDbwaPv/8c6F79+7CsWPH1G4/efjwoapNY/9sv/rqK+Gvv/4SkpKShPj4eGH9+vVCly5dhPXr1wuC0Pj7p0vFWfGNvZ8RERGqz/Hy5cvC1KlThS5duggxMTGCIDT+/gmCIMTGxgpdunQRPv/8c+HWrVvCsWPHhODgYGHx4sWqNqbQT0EQhNLSUmHgwIHCrFmzNOoM2Ucmdj0OHTokDB06VOjSpYswYMAAYdu2bcYOqVb++usvoUOHDhqv8rdhnD9/XnjppZeELl26CKGhocK3335rxIirT1v/OnToIEyfPl2tXWP+bD/99FOhf//+gp+fn/Dkk08Kr776qrBr1y61No25f7pUTOyC0Lj7OXXqVCE0NFTo0qWLEBwcLLz99ttq93cLQuPuX5njx48LL7zwguDn5ycMGDBAWL58uSCXy9XamEI/z5w5I3To0EG4dOmS1npD9ZGPbSUiIjIhvMZORERkQpjYiYiITAgTOxERkQlhYiciIjIhTOxEREQmhImdiMgIioqKUFhYaOwwyAQxsRMRGUBCQgLmzJmD/v37o2vXrujevTsiIyONHRaZIN7HTg3G8uXLsWLFCtV7iUQCT09P9O/fH5MmTYKDg4MRoyOquaioKLz99tvw8fHBuHHj0Lx5cwBAq1at1B4nTFQX+BAYalDEYjF++uknAIBCocDVq1cRGRmJO3fuYO3atUaOjqj65HI5Zs6ciYCAAHz77bcwNzc3dkhk4pjYqcHp3r276s9PPPEECgoKsHz5chQWFsLa2tp4gRHVwF9//YU7d+5g/fr1TOpkELzGTg2era0tSktL1Z4O1b9/f8yaNQsbN25Ev3790LVrV7z11luqx12W9+OPP2Lo0KHw8/NDSEgIFixYALlcrqo/e/YsfH194efnh+zsbLVt//Of/8DX1xdjxoxRK9++fTv+7//+D926dYOvr6/qdffu3Ur78vDhQ8yZMwdPPfUU/Pz8MGzYMOzevVutzebNm9G1a1ecP39eVbZ8+XL0799f9b6oqAgvv/wyXn/9dVVfdu7cCV9fX7V9XblyBZ06dVLbtsyMGTPUYi97lT9uYmIiPv74Yzz99NPo2rUrBg4ciEWLFqGoqEhtX76+vli1apVa2f379+Hr64udO3eqyvr374/ly5ertZs4caJGuwcPHmDWrFno06cPOnXqpIrtzTff1Pp7rUm8ZS8/Pz8MGjQIP/74o6r+zTff1Pq7KXuV78Off/6Jl156Cf7+/ujZsyc+/vhjpKenq+rj4+Ph5uaGvXv3YtCgQfD398fAgQOxfv16lF0JzcrKgp+fHzZv3qzRp/DwcAwePFj1Xi6XY8WKFRg0aJDq7/SHH36IvLy8av0OyHTxjJ0anOLiYgDKofhr167hhx9+QGhoKGxtbdXanThxAlevXsWsWbMgk8mwdOlSjBs3Dr/++qvqzGjhwoXYtGkTxo8fjyeffBK3b9/G119/jbS0NHz99ddq+7O2tsauXbswfvx4AMr/QPfs2aNxbf/cuXOYPXs2XnzxRcyePRuWlpY4efKkRsKqqKSkBO+88w5u3ryJqVOnomXLljhw4ACmT58OuVyOV199FQDw+uuvIzU1Fe+//z5++ukn+Pj4aOxn6tSpKCwsxPfff1/pWWBERAREIpHOek9PT3zzzTcAlF8CPv/8c7X6tLQ0eHt7Y/DgwbC3t0dCQgJWrlyJlJQU1Xa1cebMGRw7dkyjfMGCBfj1118xffp0dOjQAWZmZpg/f77e/VUn3okTJ6Jfv3549OgRduzYgS+++AKtW7dGSEgI5s6di/z8fADA0aNH8e2332Lr1q2qbT09PVV1ZfuZPHkysrKysHTpUrz55pvYtWsXrK2tUVhYiPT0dKxcuRKTJk2Cn58fTp48iYULF+LBgweYOnUqXFxcEBYWhh07duD1119XHefhw4f47bff8MEHH6jKpkyZgpMnT2LChAl44oknkJeXh2PHjqGwsBB2dnb1/plRw8fETg1KSUkJunTpolbWpUsXLFy4UKNtbm4udu3aBRcXFwBAu3bt8Pzzz2PXrl0YMWIEkpOTsXHjRkybNg3jxo0DAAQHB8POzg7Tpk3D+++/j3bt2qn299xzz2Hbtm2qxP7rr7/Cw8NDI7FfvnwZAPDZZ5/B0tISAHDnzh29fTt27BguXLiAZcuW4dlnnwUA9OnTB5mZmYiMjMQrr7yiSsIff/wx7t+/j7ffflstoQDAvHnzEBsbi61bt1Y6ofDXX3/F5cuX8fzzz+Ps2bMa9QqFApaWlqpLH2XPci+vV69e6NWrFwBAEAQEBgbC3t4eH330EbKzs+Hs7Ky337qUlpZiwYIFeOWVV7Blyxa1upiYGPTt2xcjR45Uldna2qKkpKTSfVYn3pYtW6r63q1bN+zbtw9xcXEICQlR+3uRkJAAQP0SUZnIyEi0b98eq1atgpmZcgC0bdu2GDlyJPbs2YNRo0apzso//PBDTJgwAQAQEhKCwsJCbNiwAePHj4e9vT1GjhyJt956C7GxsfDz8wMA7N27FyUlJXjhhRcAAKdPn8aff/6J+fPn45VXXlHFUf6Mvj4/M2ocOBRPDYpYLMaOHTuwY8cObN26FYsWLUJBQQEmTJigMZT4xBNPqJI6AHTs2BGtW7fGxYsXASjPBktLSzF06FAUFxerXiEhIQCUM5XLCwsLQ15eHv7++28AyuH2ESNGaMRYNqN5y5YtyM/PR3FxMapyc8m5c+cglUoxaNAgtfKhQ4ciIyND7TKCSCTC/Pnz8eDBA7z77ruq+53LzhzDw8Ph7e2t81hyuRyLFy/GmDFj4OXlpbVNQUEBrKysKo1ZLpdj5cqVGDRoELp27YouXbpg6tSpEAQBSUlJam1LS0vVfs/6kvCOHTuQkpKidjZapnnz5jh//jxiY2Mhl8ur/DuuSbz5+fn48ccfIRaL0aNHD73HKFNQUICrV69iyJAhqqQOAAEBAfD29la7pAEAw4YNU3s/dOhQyGQy1RfFXr16oXXr1ti2bZuqzbZt2xAWFqZKxqdPn4ZUKsWLL75YJ78DMk08Y6cGx9/fX/Xn7t27w8fHBy+99BJ27typNkyp7czDxcUFGRkZAJTXLQHlWbE2ubm5au8lEgleeOEFbN26FW5uboiJicHKlSvx66+/qrUbOHAgRo8ejaVLlyIiIqLK/Xr48CFcXFzUkgAAuLq6qurLK7s7QC6XY9OmTQCAlStXws/PD+vXr8eQIUMgkWj/J7xx40bIZDK8++67WL9+vdY26enpcHNzqzTmJUuW4KeffsJ7772HgIAA2NnZ4erVq5g7d67GGf7y5cv1Xo4ok5+fj2+++QYTJ07U+jnOnDkT4eHheOmll9TKn3zyyTqLd9asWZg1axYA5RfK999/X+tZuS55eXkQBEH1+ZXn6uqKBw8eAIDqMyr/JbSsDaD+uY8cORLLly/HjBkzEB8fj+vXr2PGjBmq+tzcXDg7O+v83Kv7OyDTxMRODV7ZsOiNGzfUyitOdAOUybxVq1YAoBqm3rRpk9YzUw8PD42yV199Fc899xzMzc0xaNAgrfcYi0QizJo1CwkJCZDJZJg+fTqOHz+ud7ERe3t7ZGdno7S0VC25Z2ZmqsULAMnJyVi+fDmmTZuGAQMGYMSIEbh//z4WLFiAp556CkOHDsWGDRvw9ttva/0drFmzBjNmzICNjY3WWEpKSpCQkICePXtWGvMvv/yC4cOHY9KkSaqysqHpikaNGqWWiLOzs/HOO+9obbt69WpYW1vrnAzXsmVLLFq0CMOGDcOUKVPw5JNPalz/r228kyZNQr9+/VBSUoK4uDgsXLgQUqlUZ8wV2dnZQSQSqT6/8jIzM9GiRQsAjxN4VlaW2t85bZ/7iy++iK+//hoHDx7ExYsX0aJFC/Tu3VtV7+TkhOzsbBQXF+tM7tX5HZBp4lA8NXhlCb3imd25c+dUZ+UAEBcXh9u3b6vOuoKDg2FmZob09HT4+/trvNzd3TWO1bp1a3Tv3h07d+5Uu4ZZ0fbt23H+/HnMnz8f/v7+quH5yjzxxBOQy+U4dOiQWvnBgwfh5uam+kICKK/fd+zYEa+99ho8PT3x8ssvw9vbGy+++CI8PDzw0UcfYeXKlUhOTtY4zrJly9C8eXONs93yzp49i6KiIp2jGWUePXqkMTlvz549Wtu6u7ur/X4rztAvc/fuXfzwww+YNm2azol/giBg5syZCAoKwvjx4+Hv76/zS0pN4/X29oa/vz+6d++OkSNH4qmnnsIvv/yi9xhlbGxs0LlzZ/zyyy9qlwkuXryIlJQU1bB+2c8DBw6obX/w4EFYWFiojVA5OjqqZugfOHAAL7/8strkx6eeegoKhULjToryqvM7INPEM3ZqcMqukRcXFyMpKUl1dlfxuqKjoyMmTJiAf/3rX5DL5Vi6dKkq+QHKVb3GjRuHTz/9FDdv3kRQUBDEYjFSUlLw559/Yvbs2VqvU3/55Ze4e/euzuutZWfOkydPRuvWravcr759+yIgIACzZs1CZmYmWrZsiYMHD+LEiROYP3++6j/wPXv24OzZs9i1a5fOGe2jRo3C3r17MXfuXI2h9p9//hnr16/XGPIvExUVhfnz58PNzQ2Wlpaq33d8fDwA4NatW+jYsSNsbW0REhKCn3/+Ge3bt0ezZs2wZ88erV8mqmPv3r0ICgrCwIEDdbbZtGkTrly5gn379lVr39WJNykpCRcvXkRxcTGuX7+O06dPa8x/0GfKlCl477338P7772PEiBGqWfGtW7dWTXhr06YN/u///g9Lly6FQqFQzYrfunUr/vWvf2mMCo0cORKvvfYaJBIJhg8frlbXu3dvPP3005g3bx5SU1MRFBSEwsJCHD16FFOmTIGHh0e9fGbUuDCxU4NSUlKimrBmZmYGd3d3dO/eHatWrULLli3V2oaGhqJ9+/aYP38+srOzERgYiM8++0ztbGXatGlo06YNfvrpJ2zYsAFSqRTe3t4IDQ2Fo6Oj1hhatGihGkbVZvbs2WjdujXGjh1brb6JxWKsXbsWS5YswYoVK5CXl4c2bdpg4cKFqiSQk5ODiIgIjB8/Hu3bt9e5L5FIhC+++AIvvvgidu/erdoeAPr166eaFa3NtGnTkJKSAgBqs87LzJkzB61bt0bPnj3x6aefoqSkBIsXL4ZYLMYzzzyDTz/9tMrD1doIgoBPPvlEZ31ycjK+/vprfPjhh1UaCSmvOvF+++23+PbbbyEWi+Hm5obnnnsO06ZNq9bx+vXrh1WrVmHFihWYNGkSrKysEBoaivDwcLXLPxEREfD09MSPP/6InJwceHt7Y8aMGRrrIwBAUFAQXFxc0L17d62jSpGRkVi1ahX27NmDtWvXwtHREU888YRqRKM+PjNqXLhWPDVK/fv3R+/evfHll18aO5RGp3///oiIiNB5fX3UqFH48MMP9V5/p/oRExODl19+GWvWrEG/fv2MHQ41QjxjJ2piOnXqpLHYT3nt27evtJ7qx/3793H79m189dVX8PHx0Tv/gUgXJnaiJmblypWV1ldl9jnVve3bt2PVqlVo164dFi9erHOOBJE+HIonIiIyIfxKSEREZEKY2ImIiEwIEzsREZEJYWInIiIyIUzsREREJuT/Aaq3yMkAq+OUAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "grid = np.linspace(-1, 70, 1000)\n", "\n", "plt.figure(figsize=(8, 5))\n", "plt.hist(wait_times, bins=50, density=True, label='Данные', range=(0, 70))\n", "plt.plot(grid, sps.expon(scale=tau).pdf(grid), lw=5, alpha=0.5, \n", " label='Плотность $Exp(\\\\tau)$', color='#FF3300')\n", "plt.xlabel('Время ожидания автобуса')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Оказывается, оставшееся время ожидания автобуса не зависит от того времени, которое уже прошло с момента прибытия предыдущего автобуса. Это свойство называется **свойством отсутствия памяти**. Среди всех абсолютно непрерывных распределений таким свойством обладает только экспоненциальное распределение. Среди всех дискретных распредений — только геометрическое.\n", "\n", "Если мы считаем, что у нас есть несколько маршрутов автобусов, причем все автобусы приходят независимо друг от друга с одинаковой интенсивностью, то количество автобусов, которое придется пропустить, имеет **геометрическое распределение**.\n", "\n", "А сколько времени проходит между каждым пятым прибывающим автобусом? Посчитаем эти интервалы времени." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "ExecuteTime": { "end_time": "2021-03-06T12:53:10.578488Z", "start_time": "2021-03-06T12:53:10.566880Z" } }, "outputs": [ { "data": { "text/plain": [ "49.99999847766274" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "intervals = np.diff(bus_arrival_times[::5])\n", "intervals.mean()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Посмотрим на гистограмму длин интервалов между прибытиями каждого 5-го автобуса и сравним ее с плотностью **гамма-распределения**." ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "ExecuteTime": { "end_time": "2021-03-06T12:53:11.865971Z", "start_time": "2021-03-06T12:53:11.448432Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "grid = np.linspace(-1, 180, 1000)\n", "\n", "plt.figure(figsize=(8, 5))\n", "plt.hist(intervals, bins=50, density=True, label='Данные', range=(0, 180))\n", "plt.plot(grid, sps.gamma(a=5, scale=tau).pdf(grid), lw=5, alpha=0.5, \n", " label='Плотность $\\\\Gamma(5, \\\\tau)$', color='#FF3300')\n", "plt.xlabel('Время между прибытиями каждого 5-го автобуса')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Этот пример также показывает, что экпоненциальное распределение является частным случаем гамма-распредедения." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 4 }