{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "#### ФИВТ МФТИ\n", "\n", "#### Курс математической статистики\n", "\n", "Никита Волков (email, VK)\n", "\n", "# Справочник по Python\n", "\n", "## Очень коротко базовые понятия Python\n", "\n", "Подробно можно прочитать в статьях:\n", "\n", "Python 2: https://habrahabr.ru/post/61905/\n", "\n", "Python 3: https://ru.wikibooks.org/wiki/Python/%D0%A3%D1%87%D0%B5%D0%B1%D0%BD%D0%B8%D0%BA_Python_3.1\n", "\n", "Арифметические операции и печать" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3 30 10.8 10 8\n" ] } ], "source": [ "print(1 + 2, 5 * 6, 54 / 5, 54 // 5, 2 ** 3)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "x = 3, y = 1.5\n" ] } ], "source": [ "x = 1\n", "x += 2\n", "y = x / 2\n", "print('x = {}, y = {}'.format(x, y))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Условные операторы" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "True\n" ] } ], "source": [ "if x > 2 and not 2 <= y < 3:\n", " print(True)\n", "else:\n", " print(False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Циклы" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "x = 10, range(5) = [0, 1, 2, 3, 4]\n" ] } ], "source": [ "x = 0\n", "for i in range(5):\n", " x += i\n", " \n", "print('x = {}, range(5) = {}'.format(x, list(range(5))))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Но тут можно и проще" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "10\n", "10\n" ] } ], "source": [ "print(sum([i for i in range(5)]))\n", "print(sum(range(5)))" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Сначала теория вероятностей\n", "Потом математическая статистика\n", "Затем случайные процессы\n" ] } ], "source": [ "order = ['Сначала', 'Потом', 'Затем']\n", "courses = ['Теория вероятностей', 'Математическая статистика', 'Случайные процессы']\n", "for preposition, course in zip(order, courses):\n", " print(preposition, course.lower())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Если у вас русский язык не работает, поставьте u перед строками.\n", "Например, u'текст'." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "16\n" ] } ], "source": [ "x = 1\n", "while x < 12:\n", " x += x\n", "print(x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Листы и туплы" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " \n" ] } ], "source": [ "x = [1, 2, 3] # лист\n", "y = (1, 2, 3) # тупл\n", "print(type(x), type(y))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Листы изменяемые" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1, 2, 3, 4]\n", "[1, 2, 3, 4, 5]\n", "[1, 2, 3, 4, 5, 1, 2, 3, 4, 5]\n" ] } ], "source": [ "x.append(4)\n", "print(x)\n", "x += [5]\n", "print(x)\n", "x = x * 2\n", "print(x)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "ename": "AttributeError", "evalue": "'tuple' object has no attribute 'append'", "output_type": "error", "traceback": [ "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[1;31mAttributeError\u001b[0m Traceback (most recent call last)", "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0my\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m4\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;31m# туплы не изменяемые\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[1;31mAttributeError\u001b[0m: 'tuple' object has no attribute 'append'" ] } ], "source": [ "y.append(4) # туплы не изменяемые" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Срезы" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[3, 4, 5]\n", "[0, 1, 2, 3, 4]\n", "[5, 6, 7, 8, 9]\n", "[1, 3, 5, 7]\n", "[0, 2, 4, 6, 8]\n", "[0, 1, 2, 3, 4, 5, 6, 7, 8]\n", "9\n" ] } ], "source": [ "x = list(range(10))\n", "print(x[3:6])\n", "print(x[:5])\n", "print(x[5:])\n", "print(x[1:9:2]) # Через один\n", "print(x[::2])\n", "print(x[:-1]) # Все, кроме последнего\n", "print(x[-1]) # Последний" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Функции" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.0782\n", "0.3989\n" ] } ], "source": [ "from math import sqrt, e, pi\n", "\n", "def normal_density(x, a, sigma):\n", " return (1 / sqrt(2 * pi * sigma ** 2)) * e ** (-(x - a) ** 2 / (2 * sigma ** 2))\n", "\n", "standart_normal_density = lambda x: normal_density(x, 0, 1)\n", "\n", "print('{:.4f}'.format(normal_density(0, 1, 5)))\n", "print('{:.4f}'.format(standart_normal_density(0)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Некоторые полезные функции" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[(0, 0), (1, 2), (2, 4), (3, 6), (4, 8)]\n", "[0, 1, 4, 9, 16]\n", "[(9, 'a'), (7, 'a'), (4, 'a'), (5, 'k'), (4, 'n'), (3, 'n'), (3, 'n')]\n" ] } ], "source": [ "# zip --- скрещивает два массива одной длины\n", "x = zip(range(5), range(0, 10, 2))\n", "print(list(x))\n", "\n", "# map --- применяет функию к каждому элементу массива\n", "x = map(lambda tmp: tmp ** 2, range(5))\n", "print(list(x))\n", "\n", "# sorted --- сортировка\n", "x = list(zip([7, 3, 4, 4, 5, 3, 9], ['a', 'n', 'n', 'a', 'k', 'n', 'a']))\n", "# сначала сортировка по букве по алфавиту, потом сортировка по убыванию по числу \n", "x = sorted(x, key=lambda element: (element[1], -element[0]))\n", "print(list(x))" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[(9, 'a'), (7, 'a'), (4, 'a'), (5, 'k'), (4, 'n'), (3, 'n'), (3, 'n')]" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Сохрание в файл и чтение" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "9 a\n", "['9', 'a']\n", "7 a\n", "['7', 'a']\n", "4 a\n", "['4', 'a']\n", "5 k\n", "['5', 'k']\n", "4 n\n", "['4', 'n']\n", "3 n\n", "['3', 'n']\n", "3 n\n", "['3', 'n']\n" ] } ], "source": [ "# Сохранение\n", "with open('example.txt', 'w') as f:\n", " for element in x:\n", " f.write(' '.join([str(element[0]), element[1]]))\n", " f.write('\\n')\n", " \n", "# Чтение\n", "with open('example.txt') as f:\n", " for line in f:\n", " print(line[:-1]) # лишний перевод строки убираем\n", " print(line[:-1].split(' '))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Некоторые полезные типы данных" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Множество (в нем элементы не упорядочены и не повторяются)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "{1, 2, 3, 4}\n", "{1, 2, 3, 4, 5}\n", "{2, 3, 4, 5}\n", "{2, 4}\n", "{3, 5}\n", "{2, 3, 4, 5, 6, 8}\n", "{3, 5, 6, 8}\n", "False\n", "True\n", "False\n", "True\n" ] } ], "source": [ "x = set([1, 4, 2, 4, 2, 1, 3, 4])\n", "print(x)\n", "\n", "x.add(5) # добавление элемента\n", "print(x)\n", "\n", "x.pop() # удаление элемента\n", "print(x)\n", "\n", "print(x.intersection(set([2, 4, 6, 8]))) # Пересечение\n", "print(x.difference(set([2, 4, 6, 8]))) # Разность\n", "print(x.union(set([2, 4, 6, 8]))) # Объединение\n", "print(x.symmetric_difference(set([2, 4, 6, 8]))) # Симметрическая разность\n", "\n", "print(x.issubset(set([2, 4, 6, 8]))) # Является ли подмножеством\n", "print(x.issubset(set(list(range(10)))))\n", "\n", "print(x.issuperset(set([2, 4, 6, 8]))) # Является ли надмножеством\n", "print(x.issuperset(set([2, 4])))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Словари\n", "\n", "Пример: словарь \"распределение - количество параметров\"" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "True False\n", "keys: dict_keys(['Normal', 'Bernoulli', 'Gamma', 'Poisson'])\n", "values: dict_values([2, 1, 2, 1])\n", "Normal имеет 2 параметра\n", "Bernoulli имеет 1 параметр\n", "Gamma имеет 2 параметра\n", "Poisson имеет 1 параметр\n" ] } ], "source": [ "x = dict()\n", "x['Normal'] = 2\n", "x['Bernoulli'] = 1\n", "x['Poisson'] = 1\n", "\n", "x['Gamma'] = 1 # если ошиблись,\n", "x['Gamma'] = 2 # то можно исправить\n", "\n", "print('Normal' in x, 'Cauchy' in x)\n", "print('keys:', x.keys())\n", "print('values:', x.values())\n", "\n", "for key in x:\n", " print('{} имеет {} параметр{}'.format(key, x[key], 'а' if x[key] == 2 else ''))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Библиотека numpy" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Самое основное — класс numpy.array" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1 2 3 4]\n" ] }, { "data": { "text/plain": [ "array([1, 2, 3, 4])" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = [1, 2, 3, 4]\n", "x = np.array(x)\n", "print(x)\n", "x" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "С ним удобно производить арифметические операции" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[2 3 4 5]\n", "[2 4 6 8]\n", "[ 0.5 1. 1.5 2. ]\n", "[1 5 8 5]\n", "[ 0 6 15 4]\n", "[ 1 4 9 16]\n" ] } ], "source": [ "print(x + 1)\n", "print(x * 2)\n", "print(x / 2)\n", "print(x + [0, 3, 5, 1])\n", "print(x * [0, 3, 5, 1])\n", "print(x ** 2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Есть встроенные функции" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "10\n", "24\n", "[ 1. 1.41421356 1.73205081 2. ]\n", "[ 2.71828183 7.3890561 20.08553692 54.59815003]\n", "[ 0. 0.69314718 1.09861229 1.38629436]\n", "[ 0.84147098 0.90929743 0.14112001 -0.7568025 ]\n", "2.718281828459045 3.141592653589793\n" ] } ], "source": [ "print(x.sum()) # или np.sum(x) --- сумма всех элементов\n", "print(x.prod()) # или np.prod(x) --- произведение всех элементов\n", "print(np.sqrt(x))\n", "print(np.exp(x))\n", "print(np.log(x))\n", "print(np.sin(x))\n", "print(np.e, np.pi)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Такие же срезы" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[3 4 5]\n", "[0 1 2 3 4]\n", "[5 6 7 8 9]\n", "[1 3 5 7]\n", "[0 2 4 6 8]\n", "[0 1 2 3 4 5 6 7 8]\n", "9\n" ] } ], "source": [ "x = np.array(range(10))\n", "print(x[3:6])\n", "print(x[:5])\n", "print(x[5:])\n", "print(x[1:9:2]) # Через один\n", "print(x[::2])\n", "print(x[:-1]) # Все, кроме последнего\n", "print(x[-1]) # Последний" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Последовательности" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0, 1, 2, 3, 4, 5, 6] [1, 2, 3, 4, 5, 6] [1, 3, 5]\n", "[0 1 2 3 4 5 6] [1 2 3 4 5 6] [1 3 5]\n", "[ 0. 1. 2. 3. 4. 5. 6. 7.] [ 1.5 2.5 3.5 4.5 5.5 6.5] [ 1.5 2.8 4.1 5.4 6.7]\n", "[ 0. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1. ]\n", "[ 1. 1.07177346 1.14869835 1.23114441 1.31950791 1.41421356\n", " 1.51571657 1.62450479 1.74110113 1.86606598 2. ]\n" ] } ], "source": [ "# стандартные range(stop) или range(start, stop[, step]), причем все параметры целочисленные\n", "print(list(range(7)), list(range(1, 7)), list(range(1, 7, 2)))\n", "\n", "# аналог из numpy, причем допускаются нецелые параметры\n", "print(np.arange(7), np.arange(1, 7), np.arange(1, 7, 2))\n", "print(np.arange(7.5), np.arange(1.5, 7.1), np.arange(1.5, 7.1, 1.3))\n", "\n", "# а если надо указывать не шаг, а количество, то\n", "print(np.linspace(0, 1, 11)) # (begin, end, count)\n", "\n", "# или можно использовать логарифмическую шкалу\n", "print(np.logspace(0, 1, 11, base=2)) # np.logspace(a, b, c, base) = base ** np.linspace(a, b, c)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Массив из нулей или из единиц" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 0. 0. 0. 0. 0.]\n", "[ 1. 1. 1. 1. 1.]\n" ] } ], "source": [ "print(np.zeros(5))\n", "print(np.ones(5))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Типы" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 0. 0.5 1. 1.5 2. 2.5 3. 3.5 4. 4.5 5. ]\n", "float64\n", "[0 0 1 1 2 2 3 3 4 4 5]\n", "['0.0' '0.5' '1.0' '1.5' '2.0' '2.5' '3.0' '3.5' '4.0' '4.5' '5.0']\n" ] } ], "source": [ "x = np.linspace(0, 5, 11)\n", "print(x)\n", "print(x.dtype)\n", "\n", "print(x.astype(int))\n", "print(x.astype(str))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Двумерные массивы\n", "\n", "Создание" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 0 1 2 3]\n", " [ 4 5 6 7]\n", " [ 8 9 10 11]]\n", "(3, 4)\n", "[[ 0 1 2]\n", " [ 3 4 5]\n", " [ 6 7 8]\n", " [ 9 10 11]]\n", "(3, 4)\n", "[ 0 1 2 3 4 5 6 7 8 9 10 11]\n" ] } ], "source": [ "X = np.arange(12).reshape(3, 4) # Создаем массив размера 12 и меняем размерность\n", "print(X)\n", "print(X.shape)\n", "\n", "print(X.reshape(4, 3)) # Можно снова изменить размер\n", "print(X.shape)\n", "print(X.ravel()) # Или растянуть его в одномерный массив" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Суммы, максимум, минимум" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "66 0 11 0\n", "[12 15 18 21] [ 0 45 120 231] [ 8 9 10 11] [0 1 2 3]\n", "[ 6 22 38] [ 0 840 7920] [ 3 7 11] [0 4 8]\n" ] } ], "source": [ "print(X.sum(), X.prod(), X.max(), X.min()) # По всему массиву\n", "print(X.sum(axis=0), X.prod(axis=0), X.max(axis=0), X.min(axis=0)) # По столбцам\n", "print(X.sum(axis=1), X.prod(axis=1), X.max(axis=1), X.min(axis=1)) # По строкам" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Арифметические операции (все операции поэлементные)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 0 1 2 3]\n", " [ 4 5 6 7]\n", " [ 8 9 10 11]]\n", "[[ 1 2 3 4]\n", " [ 5 6 7 8]\n", " [ 9 10 11 12]]\n", "[[ 0 2 4 6]\n", " [ 8 10 12 14]\n", " [16 18 20 22]]\n", "[[ 0 1 3 4]\n", " [ 4 5 7 8]\n", " [ 8 9 11 12]]\n", "[[ 0 1 2 3]\n", " [ 4 5 6 7]\n", " [10 11 12 13]]\n", "[[ 0 2 4 6]\n", " [ 8 10 12 14]\n", " [16 18 20 22]]\n", "[[ 0 1 4 9]\n", " [ 16 25 36 49]\n", " [ 64 81 100 121]]\n" ] } ], "source": [ "print(X)\n", "print(X + 1)\n", "print(X * 2)\n", "print(X + [0, 0, 1, 1]) # второе слагаемое дополняется до матрицы копированием строк\n", "print(X + np.array([[0, 0, 2]]).T) # .T - транспонирование\n", "print(X + X)\n", "print(X * X) # только одного размера" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "А вот так уже не получится" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "ename": "ValueError", "evalue": "operands could not be broadcast together with shapes (4,3) (3,4) ", "output_type": "error", "traceback": [ "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[1;31mValueError\u001b[0m Traceback (most recent call last)", "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mX\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mT\u001b[0m \u001b[1;33m*\u001b[0m \u001b[0mX\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;31m# размеры не совпадают\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[1;31mValueError\u001b[0m: operands could not be broadcast together with shapes (4,3) (3,4) " ] } ], "source": [ "print(X.T * X) # размеры не совпадают" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Для этого есть класс numpy.matrix, в котором операция умножения определена как матричное умножение" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 80 92 104 116]\n", " [ 92 107 122 137]\n", " [104 122 140 158]\n", " [116 137 158 179]]\n" ] } ], "source": [ "X = np.matrix(X) # Преобразование типов\n", "print(X.T * X)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Зато тут уже поэлементно не получится" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false }, "outputs": [ { "ename": "ValueError", "evalue": "shapes (3,4) and (3,4) not aligned: 4 (dim 1) != 3 (dim 0)", "output_type": "error", "traceback": [ "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[1;31mValueError\u001b[0m Traceback (most recent call last)", "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mX\u001b[0m \u001b[1;33m*\u001b[0m \u001b[0mX\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[1;32m/usr/local/lib/python3.4/dist-packages/numpy/matrixlib/defmatrix.py\u001b[0m in \u001b[0;36m__mul__\u001b[1;34m(self, other)\u001b[0m\n\u001b[0;32m 341\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mother\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mN\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mndarray\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlist\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtuple\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 342\u001b[0m \u001b[1;31m# This promotes 1-D vectors to row vectors\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 343\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mN\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0masmatrix\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mother\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 344\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0misscalar\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mother\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mor\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mhasattr\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mother\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'__rmul__'\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 345\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mN\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mother\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", "\u001b[1;31mValueError\u001b[0m: shapes (3,4) and (3,4) not aligned: 4 (dim 1) != 3 (dim 0)" ] } ], "source": [ "print(X * X)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Многомерные массивы" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[[ 0 1 2 3]\n", " [ 4 5 6 7]\n", " [ 8 9 10 11]]\n", "\n", " [[12 13 14 15]\n", " [16 17 18 19]\n", " [20 21 22 23]]]\n" ] } ], "source": [ "X = np.arange(24).reshape(2, 3, 4)\n", "print(X)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Суммирование (аналогично остальные)" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[12 14 16 18]\n", " [20 22 24 26]\n", " [28 30 32 34]]\n", "[ 66 210]\n" ] } ], "source": [ "# суммируем только по нулевой оси, то есть для фиксированных j и k суммируем только элементы с индексами (*, j, k)\n", "print(X.sum(axis=0))\n", "# суммируем сразу по двум осям, то есть для фиксированной i суммируем только элементы с индексами (i, *, *)\n", "print(X.sum(axis=(1, 2)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Сортировка" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 1 2 3 3 3 4 5 6 6 7 8 10]\n", "[[ 2 6 3 7]\n", " [ 1 4 3 8]\n", " [10 5 6 3]]\n", "[[ 2 3 6 7]\n", " [ 1 3 4 8]\n", " [ 3 5 6 10]]\n" ] } ], "source": [ "X = np.array([2, 6, 3, 7, 1, 4, 3, 8, 10, 5, 6, 3])\n", "print(np.sort(X, kind='mergesort'))\n", "\n", "X = X.reshape(3, 4)\n", "print(X)\n", "X = np.sort(X, axis=1, kind='quicksort') # сортировка тут только по одной координате. По нескольким нельзя\n", "print(X)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Сохранение в файл и чтение из файла" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false }, "outputs": [], "source": [ "x = np.arange(0, 25, 0.5).reshape((5, 10))\n", "\n", "# Сохраняем в файл example.txt данные x в формате с двумя точками после запятой и разделителем ';'\n", "np.savetxt('example.txt', x, fmt='%.2f', delimiter=';')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Получится такой файл" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.00;0.50;1.00;1.50;2.00;2.50;3.00;3.50;4.00;4.50\n", "5.00;5.50;6.00;6.50;7.00;7.50;8.00;8.50;9.00;9.50\n", "10.00;10.50;11.00;11.50;12.00;12.50;13.00;13.50;14.00;14.50\n", "15.00;15.50;16.00;16.50;17.00;17.50;18.00;18.50;19.00;19.50\n", "20.00;20.50;21.00;21.50;22.00;22.50;23.00;23.50;24.00;24.50\n" ] } ], "source": [ "with open('example.txt') as f:\n", " print(''.join(f.readlines())[:-1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Теперь его можно прочитать" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 0. 0.5 1. 1.5 2. 2.5 3. 3.5 4. 4.5]\n", " [ 5. 5.5 6. 6.5 7. 7.5 8. 8.5 9. 9.5]\n", " [ 10. 10.5 11. 11.5 12. 12.5 13. 13.5 14. 14.5]\n", " [ 15. 15.5 16. 16.5 17. 17.5 18. 18.5 19. 19.5]\n", " [ 20. 20.5 21. 21.5 22. 22.5 23. 23.5 24. 24.5]]\n" ] } ], "source": [ "x = np.loadtxt('example.txt', delimiter=';')\n", "print(x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Библиотека scipy (модуль scipy.stats)\n", "\n", "Нам пригодится только модуль scipy.stats.\n", "Полное описание http://docs.scipy.org/doc/scipy/reference/stats.html" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import scipy.stats as sps" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Общий принцип:\n", "\n", "$X$ — некоторое распределение с параметрами params\n", "
\n", "
• $X$.rvs(size=$N$, params) — генерация выборки размера $N$ (Random VariateS). Возвращает numpy.array
• \n", "
• $X$.cdf($x$, params) — значение функции распределения в точке $x$ (Cumulative Distribution Function)
• \n", "
• $X$.logcdf($x$, params) — значение логарифма функции распределения в точке $x$
• \n", "
• $X$.ppf($q$, params) — $q$-квантиль (Percent Point Function)
• \n", "
• $X$.mean(params) — математическое ожидание
• \n", "
• $X$.median(params) — медиана
• \n", "
• $X$.var(params) — дисперсия (Variance)
• \n", "
• $X$.std(params) — стандартное отклонение = корень из дисперсии (Standard Deviation)
• \n", "
\n", "\n", "Кроме того для непрерывных распределений определены функции\n", "
\n", "
• $X$.pdf($x$, params) — значение плотности в точке $x$ (Probability Density Function)
• \n", "
• $X$.logpdf($x$, params) — значение логарифма плотности в точке $x$
• \n", "
\n", "\n", "А для дискретных\n", "
\n", "
• $X$.pmf($k$, params) — значение дискретной плотности в точке $k$ (Probability Mass Function)
• \n", "
• $X$.logpdf($k$, params) — значение логарифма дискретной плотности в точке $k$
• \n", "
\n", "\n", "Параметры могут быть следующими:\n", "
\n", "
• loc — параметр сдвига
• \n", "
• scale — параметр масштаба
• \n", "
• и другие параметры (например, $n$ и $p$ для биномиального)
• \n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Для примера сгенерируем выборку размера $N = 200$ из распределения $\\mathscr{N}(1, 9)$ и посчитаем некоторые статистики.\n", "В терминах выше описанных функций у нас $X$ = sps.norm, а params = (loc=1, scale=3)." ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Первые 10 значений выборки:\n", " [-2.06235463 1.59369232 -0.68126487 2.98438357 -1.24908635 2.03774639\n", " 0.27700922 -0.89751906 3.70360346 3.74723375]\n", "Выборочное среденее: 0.777590388762\n", "Выборочная дисперсия: 8.90997270912\n" ] } ], "source": [ "sample = sps.norm.rvs(size=200, loc=1, scale=3)\n", "print('Первые 10 значений выборки:\\n', sample[:10])\n", "print('Выборочное среденее:', sample.mean())\n", "print('Выборочная дисперсия:', sample.var())" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Плотность:\t\t [ 0.10648267 0.12579441 0.13298076 0.12579441 0.10648267]\n", "Функция распределения:\t [ 0.25249254 0.36944134 0.5 0.63055866 0.74750746]\n" ] } ], "source": [ "print('Плотность:\\t\\t', sps.norm.pdf([-1, 0, 1, 2, 3], loc=1, scale=3))\n", "print('Функция распределения:\\t', sps.norm.cdf([-1, 0, 1, 2, 3], loc=1, scale=3))" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Квантили: [-3.93456088 -2.8446547 1. 4.8446547 5.93456088]\n" ] } ], "source": [ "print('Квантили:', sps.norm.ppf([0.05, 0.1, 0.5, 0.9, 0.95], loc=1, scale=3))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Cгенерируем выборку размера $N = 200$ из распределения $Bin(10, 0.6)$ и посчитаем некоторые статистики.\n", "В терминах выше описанных функций у нас $X$ = sps.binom, а params = (n=10, p=0.6)." ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Первые 10 значений выборки:\n", " [6 8 7 7 6 7 8 7 5 7]\n", "Выборочное среденее: 6.135\n", "Выборочная дисперсия: 2.466775\n" ] } ], "source": [ "sample = sps.binom.rvs(size=200, n=10, p=0.6)\n", "print('Первые 10 значений выборки:\\n', sample[:10])\n", "print('Выборочное среденее:', sample.mean())\n", "print('Выборочная дисперсия:', sample.var())" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Дискретная плотность:\t [ 0.00000000e+00 1.04857600e-04 2.00658125e-01 0.00000000e+00\n", " 6.04661760e-03]\n", "Функция распределения:\t [ 0.00000000e+00 1.04857600e-04 3.66896742e-01 3.66896742e-01\n", " 1.00000000e+00]\n" ] } ], "source": [ "print('Дискретная плотность:\\t', sps.binom.pmf([-1, 0, 5, 5.5, 10], n=10, p=0.6))\n", "print('Функция распределения:\\t', sps.binom.cdf([-1, 0, 5, 5.5, 10], n=10, p=0.6))" ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Квантили: [ 3. 4. 6. 8. 8.]\n" ] } ], "source": [ "print('Квантили:', sps.binom.ppf([0.05, 0.1, 0.5, 0.9, 0.95], n=10, p=0.6))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Отдельно есть класс для многомерного нормального распределения.\n", "Для примера сгенерируем выборку размера $N=200$ из распределения $\\mathscr{N} \\left( \\begin{pmatrix} 1 \\\\ 1 \\end{pmatrix}, \\begin{pmatrix} 2 & 1 \\\\ 1 & 2 \\end{pmatrix} \\right)$." ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Первые 10 значений выборки:\n", " [[-0.27215325 -1.38637727]\n", " [-0.31050738 1.19181083]\n", " [ 1.89454062 1.05519067]\n", " [ 0.7639327 2.23128074]\n", " [-1.31920707 -0.31138659]\n", " [-0.13399183 -0.80243711]\n", " [-0.23527991 2.35924247]\n", " [ 0.58234234 0.95402281]\n", " [ 3.24374171 3.34295157]\n", " [ 0.67813213 2.21140736]]\n", "Выборочное среденее: [ 0.87504233 1.05920753]\n", "Выборочная матрица ковариаций:\n", " [[ 1.71268537 0.85696209]\n", " [ 0.85696209 1.89059004]]\n" ] } ], "source": [ "sample = sps.multivariate_normal.rvs(mean=[1, 1], cov=[[2, 1], [1, 2]], size=200)\n", "print('Первые 10 значений выборки:\\n', sample[:10])\n", "print('Выборочное среденее:', sample.mean(axis=0))\n", "print('Выборочная матрица ковариаций:\\n', np.cov(sample.T))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Некоторая хитрость :)" ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 0.05653714 0.98363644 2.11329714 2.95404412 4.21877038 5.03033628\n", " 6.12153382 7.02678976 8.06310136 9.10200457]\n" ] } ], "source": [ "sample = sps.norm.rvs(size=10, loc=np.arange(10), scale=0.1)\n", "print(sample)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Бывает так, что надо сгенерировать выборку из распределения, которого нет в scipy.stats.\n", "Для этого надо создать класс, который будет наследоваться от класса rv_continuous для непрерывных случайных величин и от класса rv_discrete для дискретных случайных величин.\n", "Пример есть на странице http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.html#scipy.stats.rv_continuous" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Для примера сгенерируем выборку из распределения с плотностью $f(x) = \\frac{4}{15} x^3 I\\{x \\in [1, 2] = [a, b]\\}$." ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Первые 10 значений выборки:\n", " [ 1.7614412 1.77230539 1.98901154 1.84270094 1.29474504 1.77433049\n", " 1.6724117 1.86960696 1.50343537 1.26115348]\n", "Выборочное среденее: 1.658129845\n", "Выборочная дисперсия: 0.0640721845104\n" ] } ], "source": [ "class cubic_gen(sps.rv_continuous):\n", " def _pdf(self, x):\n", " return 4 * x ** 3 / 15\n", "cubic = cubic_gen(a=1, b=2, name='cubic')\n", "\n", "sample = cubic.rvs(size=200)\n", "print('Первые 10 значений выборки:\\n', sample[:10])\n", "print('Выборочное среденее:', sample.mean())\n", "print('Выборочная дисперсия:', sample.var())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Если дискретная случайная величина может принимать небольшое число значений, то можно не создавать новый класс, как показано выше, а явно указать эти значения и из вероятности." ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Первые 10 значений выборки:\n", " [1 1 3 1 3 1 1 1 1 1]\n", "Выборочное среденее: 1.865\n", "Частота значений по выборке: 0.53 0.075 0.395\n" ] } ], "source": [ "some_distribution = sps.rv_discrete(name='some_distribution', values=([1, 2, 3], [0.6, 0.1, 0.3]))\n", "\n", "sample = some_distribution.rvs(size=200)\n", "print('Первые 10 значений выборки:\\n', sample[:10])\n", "print('Выборочное среденее:', sample.mean())\n", "print('Частота значений по выборке:', (sample == 1).mean(), (sample == 2).mean(), (sample == 3).mean())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Библиотека matplotlib\n", "\n", "http://matplotlib.org/gallery.html (англ.) — тысячи примеров" ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Для того, чтобы графики рисовались прямо в ноутбуке, нужно выполнить команду" ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "%pylab inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Сгенерируем выборку из стандартного нормального распределения.\n", "Нанесем на график точки выборки." ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sample = sps.norm.rvs(size=200)\n", "\n", "plt.figure(figsize=(10, 1)) # размер графика\n", "plt.scatter(sample, np.zeros(200), alpha=0.2) # alpha - прозрачность точки\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Можно добавить график плотности" ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Hiy6Cdeu8jkYk4JRkifgjLw/OPhvuusvVxBKRll14oZt9e+65sH2719GIBJTG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\nWEaO7M7atfvIy6vl2We/ICQ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "grid = np.linspace(-3, 3, 100) # задаем сетку для построения графика плотности\n", "\n", "plt.figure(figsize=(10, 4))\n", "plt.scatter(sample, np.zeros(200) - 0.02, alpha=0.2, label='sample') # label - описание в легенде\n", "plt.plot(grid, sps.norm.pdf(grid), color='red', label='density') # color - цвет графика\n", "plt.legend() # добавляет легенду\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Предположим, что выборка приходит постепенно.\n", "Для каждого момента времени посчитаем выборочное среднее и доверительный интервал.\n", "Нанесем их на график." ] }, { "cell_type": "code", "execution_count": 55, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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uYNdKQqxeSXbRKbl4RERbjd+XRItY1p9aym5T1pw6VeHIkSMcHbCJVieS2/XE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\nU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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "time = np.arange(1, 201)\n", "means = sample.cumsum() / np.arange(1, 201)\n", "\n", "plt.figure(figsize=(15, 8))\n", "plt.scatter(time, sample, alpha=0.2, s=40, label='sample') # s - размер точек\n", "plt.plot(time, means, color='red', linewidth=2.5, label='sample mean $\\overline{X}$') # linewidth - толщина линии\n", "# заполняет пространство между двумя функциями\n", "plt.fill_between(time, means + 2 / np.sqrt(time), means - 2 / np.sqrt(time), alpha=0.1)\n", "plt.legend()\n", "plt.xlim((1, 200)) # размеры графика по горизонтальной оси (ставим None, если по стороне ограничений нет)\n", "plt.ylim((-3, 3)) # размеры графика по вертикальной оси \n", "plt.xlabel('Time') # название горизонтальной оси (аналогично plt.ylabel)\n", "plt.title('Sample by time') # имя графика\n", "plt.grid() # добавляем сетку\n", "plt.savefig('example.png') # сохранение в файл\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Посмотрим еще на то, как можно закрашивать график в соответствии с какой-то функцией.\n", "Для примера возьмем плотность распределения $\\mathscr{N} \\left( \\begin{pmatrix} 0 \\\\ 0 \\end{pmatrix}, \\begin{pmatrix} 2 & 1 \\\\ 1 & 2 \\end{pmatrix} \\right)$." ] }, { "cell_type": "code", "execution_count": 56, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/usr/local/lib/python3.4/dist-packages/matplotlib/collections.py:650: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison\n", " if self._edgecolors_original != str('face'):\n" ] }, { "data": { "image/png": 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ttUVcc00vzjuvI6tWbefkk19i8uSV1KpVhc6dm1CrlvNN/LeikVOnrqJRo5p0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\nqEg1utCV1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MNYOP8oGDMc1mvbcL9SwlrLn//8IrfcMoPJk09h1123SDukskEzLEIIIUQz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\n0nWqlNE1SGtYcsYYcygwDDjaWrsq7XhSp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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "grid = np.mgrid[-3:3:0.05, -3:3:0.05]\n", "density = np.array([[sps.multivariate_normal.pdf((grid[0, i, j], grid[1, i, j]), mean=[0, 0], cov=[[2, 1], [1, 2]])\n", " for i in range(grid[0].shape[0])]\n", " for j in range(grid[0].shape[1])])\n", "\n", "plt.figure(figsize=(14, 6))\n", "\n", "subplot(1, 2, 1)\n", "plt.pcolormesh(grid[0], grid[1], density, cmap='Oranges') # закрасить с интенсивностью density, cmap - цветовая схема\n", "plt.xlim((np.min(grid[0]) + 0.2, np.max(grid[0]) - 0.2))\n", "plt.ylim((np.min(grid[1]) + 0.2, np.max(grid[1]) - 0.2))\n", "plt.title('Gaussian density')\n", "\n", "subplot(1, 2, 2)\n", "CS = plt.contour(grid[0], grid[1], density, [0.005, 0.02, 0.05, 0.085]) # нарисовать указанные линии уровня\n", "plt.clabel(CS, fontsize=14, inline=1, fmt='%1.3f')\n", "plt.xlim((np.min(grid[0]), np.max(grid[0])))\n", "plt.ylim((np.min(grid[1]), np.max(grid[1])))\n", " \n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Итак, функции отрисовки\n", "
\n", "
• plt.scatter(x, y, params) — нарисовать точки с координатами из $x$ по горизонтальной оси и из $y$ по вертикальной оси
• \n", "
• plt.plot(x, y, params) — нарисовать график по точкам с координатами из $x$ по горизонтальной оси и из $y$ по вертикальной оси. Точки будут соединятся в том порядке, в котором они указаны в этих массивах.
• \n", "
• plt.fill_between(x, y1, y2, params) — закрасить пространство между $y_1$ и $y_2$ по координатам из $x$.
• \n", "
• plt.pcolormesh(x1, x1, y, params) — закрасить пространство в соответствии с интенсивностью $y$.
• \n", "
• plt.contour(x1, x1, y, lines) — нарисовать линии уровня. Затем нужно применить plt.clabel
• \n", "
\n", "\n", "Вспомогательные функции\n", "
\n", "
• plt.figure(figsize=(x, y)) — создать график размера $(x, y)$
• \n", "
• plt.show() — показать график.
• \n", "
• plt.subplot(...) — добавить подграфик
• \n", "
• plt.xlim(x_min, x_max) — установить пределы графика по горизонтальной оси
• \n", "
• plt.ylim(y_min, y_max) — установить пределы графика по вертикальной оси
• \n", "
• plt.title(name) — установить имя графика
• \n", "
• plt.xlabel(name) — установить название горизонтальной оси
• \n", "
• plt.ylabel(name) — установить название вертикальной оси
• \n", "
• plt.legend(loc=...) — сделать легенду в позиции loc
• \n", "
• plt.grid() — добавить сетку на график
• \n", "
• plt.savefig(filename) — сохранить график в файл
• \n", "
\n", "\n", "Посмотрим еще, как рисовать 3D-графики" ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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yOlV3J9tGshY0BgDXdbemoPGy7Mq1mXScuzIGu4YQovKTLCllaRcuhVVFyVqP\nSkqJwWCAIAgKi6NKouzJe5S8+qOL2axufzaNCyFkN4graKxcltW9bDQazdXYqqLYqiJZxBPPYfWQ\nzjfL7kJuiO7Vi98J8UMAfgNAHcDvSSnfa2jzWwDeBGAA4D9IKZ+aff+zAP4nAALA70opfzNp/xRW\nFSMujiqKiqMKggCNRgMHBwe8eRaE7vbX7XbDTF5J8NwQsl2oxBBVRD1XGo1GeIzRgsau6251QWNa\na6bwhV5V2Z3zKoSoA3gAwJ0ALgH4ghDiYSnl01qbuwHcIKW8UQhxB4APAHi9EOJfYSqqbgcwAfBp\nIcQfSym/Erc/CquKsGo9qkajUbqVSqfKFqtoUhCb3f5M2HZuCCHlERUethc0JmaSBORkMtnpEh+V\nZree5d8H4Fkp5XMAIIT4GIAfBvC01uY8gA8BgJTyCSHEGSHEywDcDOAJKeVotu6fAvhRAL8WtzP+\nYracLHFUClMcVb/ft2qybOPkfd3+bCIpiI3jUjQcA0K2i20uaEyLFWtYVZudepaeBXBR+/w8gDsy\ntLkWwF8B+GUhxIsAjAD8ewBPJu2MwmpLUW4XWeKokupR2ThZtak/6z5YVRFmKSV6vV4mtz+SDTUp\nYywHIcWyzj2aBY3tIklAnpycMNV6VbFonlUAWQ924YcgpfyyEOK9AD4LwAHwFIAgaSMUVltINDFF\nWhxVWj0qG4WMLW8LVxWeQRBgOBzCdV3s7e2h3W6vdTxCiDDtcVnYIsL1TIr1ej10L9JjOQCUPl5k\nt7Hht5I3m7pHxxU0LlNs2fIMypukWMB+v8/iwJWlOvenz33+MXzu848lNbkE4Drt83WYWqSS2pyb\nfQcp5e8D+H0AEEL8HwD+IWlnFFZbxKpxVEmuZ7Y9OGzrz7JIKTEejzEcDtFqtVgLbMNIKXF8fBxm\nUvQ8LxR8unuR+vM8L5yA8Y03KRpea6sTJ7ZY0Lg4Tk5OKKyqSnV0Fd74b96AN/6bN4Sf//df+c/R\nJl8EcKMQ4noAXwfwVgA/HmnzMID7AXxMCPF6AJellC8AgBDipVLKbwghXg7gR7DoRjgHhdUWsG4c\nVRK2WCF0VJ9seDAuMz6e58FxHAghNl4LzJbzVFYfgiAIXSq73S5ardZcX6LuRaPRKJxoRd94Rydh\nFL6EbAdJBY11Tw5gsaDxsr9zW55BeZN0nLRYVZny5xNFIaX0hBD3A/gMpunWPyilfFoIcd9s+YNS\nykeEEHfLX/jMAAAgAElEQVQLIZ7F1OXvXdomPiGEeDGmWQF/Rkp5JWl/FFYWo97C665Oq8RRJWGD\ni9m2oyb9k8kE+/v7VmVZ3CRlHFPUAggg/DeNtDfeqtCp+l1VtdApIZvGJtERFU1xBY35O18eWqxI\nVZBSfgrApyLfPRj5fH/Muv92mX1RWFnKMgV+VRxVu93G0dHRUg8LWywhOjb1Kakv+qS/3W7jzJkz\nuT2obRqTolDWVyEEDg8PIYSA67prbTP6xrtqtXe2DZsm6KQa6Gnf9YLGUbGlChrvuthKS17BrIAV\nZcfmE0VCYWUZq8ZRHR4ezr2Zz4qNE3ab+hTXl+ikf5Wx30aKOC964g/dApiHZXXZ2jvMUEayQtFo\nD0liK+6livrNV/08Jh2f4zi4+uqrC+4RKQY75lhVhMLKEvKMoyKbQ3e53N/fR7PZLOSha4PYzPs4\n9ZcFpsQfRY3BMumgGa9FdpEqiI20lyrq9+44Tvjb3jULNl0BK4wlL6+rCGfkJaNu5JPJJHxYbTqO\nKgkbJuxRbOqTspToKb5Xcbkkyej1vpZ5WRB3DjZ9DZnitaJFThnHQch2o//Ofd9HvV5Ho9GItWDb\nVNB4VZi8YlexY45VRSisSqSoOKokbBIxCtv65Pv+XIrvMtz+bBiTPPqgX9ubqPdVJGoyleZaVJUJ\nGCGKsu9FRZLFgq2e49Hfue2/9bTzSGFVYXboN1w0FFYlUHQcVRI2TNhN2NAn3/cxHo/h+z56vV7m\nbHQkHSll6NLaaDSWqvdlqxtSlngt0wSM8VpkG6n69Zp0n7GxoPE6JCWvoLCqKuXPsaoKhVWBqLfZ\nk8kEQLygAubjqHq9XvimbNPYKKzKfujoVpRms4larVa6qLLxPK2K7/sYDAYIggDdbjfztV32dbEK\naW+7k4qcMl5ru7H1BQDJh20saJx2jfb7fRwdHRXYI1IYFZlP2AiFVQGoiZQKgm00GrE3szziqJKw\nccJeVp+UhXA4HIZWFM/zMB6PC++Ljax7XvQ4tU6ng06ns/a1vY2T12XitfQJGCG2sI2/u2XZxDGa\nChpHa+mpGF4bX6z0+32mW68sds37qgSFVc7oN8/xeBw7mcwzjioLNj0oyxBWevIE3Ypio/DcRiaT\nCRzHKTVOzWbS4rWUuB8MBqEo24YYDkLIPCaxVVYinLTnvu/7zDpcUTivyQ/+YnLCFEelamJE2+Ud\nR5XErk/K9JpJNidPsEngLSPCgyDAYDAI09OX7VK5LZjitfr9Ptrtdii4XNfFyw43cQuXOPE7G9gO\nIdWhyJeNcS9WbChobOPzkBCbobDKEfXWSd2YopPjouKo0lD9suUGWoSISKuZVGRftoVlrg8pJcbj\nMYbD4UYtsKZr1XTtVvW8XdX2Zv8T2OTt+6A+mv4nHDOJk2B/Y9uPo4rnSGHTPXXTVPnYbGCVgsar\n1NhKOo9qf6Sq8NzmBYVVTpgsVGqyV3QcVZa+2nQDVbWj8sLzPDiOA2B7Cizbdo6SUC8MhBC5WmDV\n5GNbxmUVDmrD6X+EwMGRuk7XuVfoY2XYjroPSbXvafs8RRYn6MRGbBOPWQoaj8fjuRIPaWIryzHa\nNAaEbAP2zygrhEoxbVuR2apPThW6259yS8vyULFpbGx72OusMr5kkYPaAHOiZ2EMTddjXBth+E59\nDMzbl4svNQ6EE27jRPYM+yeEFE1S2vcsBY2TUKniSUWxaF5TNfiryRE1qVRuUePxGFJKHB4eYn9/\n36pJp03iYdNiRmWjOz4+BgAcHR1ljqWyRVjZcq2YxkNd36uMLznloDZYFFXA9AGo/mKR2l+W703b\nD4yiKrrfA9HHAfoJfSFVx+YXPJvAhnv+qiix1Ww20el0sL+/j263i3a7jVqtFtZndBwndCdUCTP0\n4+73+9jf37yl+tOf/jRuuukm3HjjjXjve99rbPOe97wHN954I2655RY89dRT4fe/8iu/gle/+tV4\nzWteg7e97W3M2LsWssJ/5UKLVc7ocVTtdhsArMuIZtsDcpNiRndL2xa3v21Cz6ZYxPjaInQ3yYHo\nA0K940r5LUaP3fTbjVqi9HWEiBFoMWO60FZM2wrgQCpxJXECFhHVqdo1uqvY9mxclTjLlnIdVMlw\nvv71r+Pd7343Xvva1+KVr3wlOp1OaO3aBL7v4/7778ejjz6Ks2fP4vbbb8f58+dx8803h20eeeQR\nPPvss3jmmWfwxBNP4N3vfjcef/xxPPfcc/jd3/1dPP3002i323jrW9+Kj33sY3jnO9+5kb7tHLxH\n5QZnmTniOA7G43EYR+W6blgc2CZsnKyu259oNrpms7nSQ9KmsbElyYgKalblAWzOpmgzB0IJk5nY\nETPRYiRmbHULk6jNPyxN123WazmpnWHRgbwCADgRrHmjw9/EdmLDfTZvVMxWo9EIs7WeO3cOv/RL\nv4QLFy7g0UcfxZ/92Z/hqquuwute9zrcdtttuP3223Hbbbfh+uuvX2l8nnzySdxwww24/vrrAQD3\n3HMPPvnJT84Jq4cffjgUS3fccQcuX76MF154AYeHh2g2m2HJicFggLNnz64/EDuLHfOaKkJXwBzp\ndDpzblE2TdJ1bOvXOg80NeE/Pj5GrVbD0dHRRmJ9bBqfsplMJjg+PkYQBDg6OtpIod9d4gAn86IK\nMFue5sjg6hD4Ceuor4J5l7/wc6SNaR+x7ohi2n8hcCCv4CC4zN9LxdkF4bELRM/j3t4efvAHfxA/\n//M/j1/4hV/AO97xDnzlK1/BL/7iL+Lw8BAf+chH8AM/8AP45V/+5ZX2d+nSJVx33XXh53PnzuHS\npUuZ2rzoRS/Cz/3cz+HlL385rr32Wpw5cwZ33nnnSv0gmHcxr9pfydBilSONRgO+fzrZsU3AKGzr\n16r9UenTN1mE1qbJQ9nnSfngj0ajuSLKNpJ3ZslVOMDJ9D9CTHWLAEIBM3deRTahFVq59K+VG2D0\nnZnhgRONp5JR0RZ2MqUrajun6x7KY3xj1F7ISmbT74kQEs+VK1dwcHCAl7zkJbjrrrtw1113hctU\nfc5lWSYNfJSvfOUr+I3f+A0899xzODo6wo/92I/hIx/5CN7+9rev1Bdiz5yvalBYFUjZE+M4bOvX\nsv3xfR+DwQC+77MIbQ4oMaUKVJYpqmy7VrNwII/nY6gS9YoeF6XHRkWEkjQJMn25P7/enIiKxF7N\nTXai7oh6Z9OEloq/mro2vrQ9BiDxjXEnFLnR4qaE2MiuWOSSjvPk5ASHh2bX3lVjac+ePYuLFy+G\nny9evIhz584ltnn++edx9uxZfO5zn8Mb3vAGvPjFLwYA/OiP/igee+wxCqtV2bLn6DZBV8Ac2aai\npbb2KwkpJQaDAa5cuYJGoxG6/W0aW85bGf1Qbn+e5+Hw8HCp4pPEIKq0fxZJGNe4jH3h8jiBZVon\nYr2K/j+6qcA3WqXMfdJdG6dtX9oa4GWdEfb29tBsNqGKc6usZJ7nwXXdhaxk20zVJ+ZVPz4yzQp4\ncLDZpDS33XYbnnnmGTz33HNwXRcf//jHcf78+bk258+fx4c//GEAwOOPP44zZ87gmmuuwStf+Uo8\n/vjjGA6HkFLi0Ucfxate9aqN9m+3iLqXV+mvXGixKhBbJuhRbOtXWn9UPbDBYIBGo5FrEdos/aki\n0eQftloBbT03B3Kaen6aUCKYiStlZdJbxtSZipuzqngo3YIVtV4tlLQyiKsFw1TErTBqnJpbnuLH\nHt3fbAyOgm/jpPGS8G23ykqm6u7o9XZ0qxZdCEnR7IpwTDrOfr+Pq6++eqP7azQaeOCBB3DXXXfB\n933ce++9uPnmm/Hggw8CAO677z7cfffdeOSRR3DDDTeg2+3ioYceAgB87/d+L37yJ38St912G2q1\nGm699Vb89E//9Eb7t1NY+NysCiJlUsKRXwNVnE8hpcR3vvMdXHXVVVbdtEejEXzfR7fbLbsrAE7H\n6UUvetHCMt/34TgOpJRhtr+8uXz5Mg4ODkp3Xbpy5Ur41j8v1GR3OByi3W5jb29v7lotog9JHB8f\no9vthpPzyWSCIAgWfk+qLkun0ym8jwfyeFGoLMQ8AcludSY3PbUoEo+Vtp7J5S/chv5dsNjPBZEk\ntO9MfYsm0DBsS0qcNF4CABiPxxBChMJdiSzf98N/pZRzQitLcdOyUcWybbmnbprhcIhms1nZ8hWe\n52EymWBvb6/sruSK4zjY29sz/p5+/dd/Ha95zWvwIz/yIyX0bKuwZzKXESGEDP7pL8vuRm7UXvav\nIaUs7bxU865oCSZXQBux9a2//jatzPTeto7PptFrfuVtBVwVm8/FQfCdU2tSXFIJHRE3vlHXvNnn\nWm3xLaNJDKn1ojWrTMkulGlKzxIYxmUpkRQRX9F159omEO5fojf5BvrNly40iau34/s+fN8PBbMQ\nwmjZIsVQdYtO1Y8vC/1+PzbGilQAS5+jeSGE+CEAvwGgDuD3pJQL1amFEL8F4E0ABgD+g5Tyqdn3\n/yuAnwAQAPgrAO+SUsZWp6awKhhbahHp2DZZ1cdGxWMMBgO0Wi0cHR1Z/7Y6T/I4T+rtuuu6oduf\nTdfnNnDgf3v6H+XyFxqEkuKmImLEJLT08x0EZqtTtCCwad2k7wIv4loYFWu6gIqKM2kWjfq2DPsX\nQqA3+QZ6NYlvy6vi15+1bTQacy6ESmwFQQDXdUMXwqhVi9cxIfGkJa/YdIwVsQl75nx5I4SoA3gA\nwJ0ALgH4ghDiYSnl01qbuwHcIKW8UQhxB4APAHi9EOJ6AD8F4GYp5VgI8XEA9wD4UNz+KKxyxHTD\nsk3EKGzrkxACk8kEo9EIUkocHByU5nZiyznb9CRxFdFqy1ikUWQ/p6JKnoqqVT1DpK9Zp0zWLM16\nZbJSBf7ielm/i4qpYBL5rIkvXVwFfrx4NLoRqvGRs3MEvEh8B31cY96GARVzpV+ryoVQuQ8qF9Gy\n4rVse3lGlmMXzl/a/ZEWK1Ihvg/As1LK5wBACPExAD8M4GmtzXnMxJKU8gkhxBkhxDUArgCYANgX\nQvgA9jEVZ7FQWBWMjRNT2x4gQRBASgnHcaywoNh4ztbF8zwMBoPSRes2c+B961RUmGKToq54pnZx\nBH5yWxnA6KKXJqRUEeEkcaUsaXFuhsC8uDK5GKr9RL+fjUl04tqbvIB+M7u4iqK7EKr4Pz1ey/d9\nuK67lfFaNrILwmNXSEpeQWFVYSo2p0nhLICL2ufnAdyRoc1ZKeUFIcT7APwDgCGAz0gpH03aGWdT\nBWPjJN2WPumJEwBwwh9hE+dJpah3XbfwWLVNYMu1euB9C/MucnpChyUz5oXLovFTvrmdvh2T++Ay\nlqtlWLBqeTC6COrbjYguqS07PY+zuCv3HwEZoN8+u1y/YjDFa0WtWtF4Lb2YMdlddkE4ph0jXQGr\nTvnP0U3xuce+iM899sWkJlkPduEHIYT4HgD/M4DrARwD+L+FEG+XUn4kbiOctebItrgC2tAnPXHC\nwcEBHMcptT86NozPuqgU9Y7joNlsrhyrVoWxWJcD75unH+bEhp4FMMOkTMoE8RQZY5MwAswJJlT7\nKP7ELNCSXABVevdoe1OyCl1oze0ii4AT4X5740sbE1dRlIUqLl5rPB4zXosQTLMF7+/vl90NkhdJ\nsbFbxhu//1a88ftvDT//x//8X6NNLgG4Tvt8HaYWqaQ252bfvRHAY1LKfwYAIcQfAHgDAAorW7Bx\nYlpmn/R6SXt7e6Hbn43jVDarjonv+xgMBgiCAL1er7RU6VWgN3kBElqcTlbXvlQ0kRW1QqlzrsSV\n6YEofcN6MenTw1gpQybA6OfQpS9OfK0RU2bq+yyrYp7iSieveK2q37uqbtGRUlbeRTTtHO7CGOw2\n1b5HRfgigBtniSi+DuCtAH480uZhAPcD+JgQ4vUALkspXxBC/C2A/00IsQdghGkCjCeTdkZhlTPR\nybCNgqGMPkkpMRqNMBqN0G63cXR0ZO2D2sZzlgU9RX2n00Gn09nIGG/jWGyC3uQF6CJCSgmBGBfA\npCGq1ZP92wPvtN3CspjYJSAiUCKiSRdjsfWqDJappHVOF2rbnxdaMu2taBjPFXEfBNAbXUS/c51h\npXyJi9dSVi3P84zxWtGU77bezwhJY1fv8TvFDp1jKaUnhLgfwGcwTbf+QSnl00KI+2bLH5RSPiKE\nuFsI8SwAB8C7Zsv+uxDiw5iKswDABQALJjEdCquCsXmSXtRbSOWSVq/XY+sl2TxOZbHMmKhsf0lj\nvGofyiQ6BrVaDUGQr0tDb/z1qagQ81aNlcci8DHNIqjOScw5jUswoVaJcw00Wa4Wtj0xx2fNbWoC\nERVXqq8RoTU/HlNxJePcFOf6FBGkeuZAUStNXEVRKd91olat0WgUijLg1M2w7N/MptmF+3IVz1uU\ntGMsKoMmKYkKuQJmQUr5KQCfinz3YOTz/THr/icA/ynrviisCsZGwVDUzVO5pPm+j/39fTSbzdh9\n2zRONvUljSAI4DhOOMatVqvsLuVK3HnZ1DmbF1Vxbm9rpFcHkt0JAy9eAMW5BkZFU6yLoW7hytCX\nKDNxZYqhkoGnWdXiCgkL7V+DuJpt3xZxFSUpXsvzvPC3WNV4rSocwy6zC+KRJLAlc5pthMIqZ0yu\ngHm/YV+FPAsX625/nU4HvV5vq27otgirpH5EXSvzHGMbxqIIeuNLM+EhEbUqTc+FbnVZRCS5zumf\nZsJExLkIxgkjIL6OlNFyNfvOlHjitDNzYknKIDwOdbxzBby1hBjL3z8MQjUq0mafe8OvAQD6e/9i\nie0Xix6vpcah0+kYU76XVV+LZGPXRYfruozFrTy78RwvAwqrErBxYpqHeFCZ6FZxSbNFzGwDekbF\nTbr9mdiVycZUVM2sVHph3NnDSGawUkXji0xCS7/GZeBH2pjSr5uz7gljQeEMJImssI/BXL+SJp1S\nWZqmH+atVkbXk5m4isscGCkq3Bs8h/7+9al9Lhs1RqaU76Z4LQBGsUVIXiT9jplqfQfYMVfAIqGw\nKhhbBcOm++X7PhzHQRAE6Ha7S7/9smmcbLEyRvuhMipOJhMrCikXgem62PTb5d740kwUIPLwUZkA\nxeJ3GZgKlM2eHyXeQnE1l6TC5KI3WRB4C8LJkJbdlIQidAGcyyLoRZJezMSVSshhsuKpZQvMXAT1\nQstCoOf8Pfrd745Zx36i8VrKhTAuXksXXDb8vnfdmrMLnJycoNfrld0NkieWzK+qCIVVzkQfQDYJ\nBp1N9UvPRLduAVobx8kG9ELKrVYLZ86cKWyiY+v1uyl6w3+YTv6VSDHVqMqRqMjJY3sm976FdgtZ\nAQ2uhXMbjaRxXygkHEO4LGZ89TgyzYK47eJKR3chNMVr6TFbVY3Xso1dEI9pFqvDw8OCe0SKpfyX\nxVWFwqpgbL5ZrzNhllKGmejWKUCrsGkCb0tfhBDwfR8nJyeQUuLg4GAhUxlZnd7wa1PxIMSim4Se\n4U5dCnG/5QQBchqnVEuIlwsAGRjd+6T0IUT9tN3cwiDSNkY0xXy3uLNIMWBNXEl/Mv0uTkDNCS3N\nJTBq3TpdAYvxVrPlumUs3F61xFUUXWzpKd9N8Vomq1aez5ldEB27QFKdKroCErI6nJXlzDZZrFbF\n8zwMBgNIKTdWgNYW9zvAjnOmrFSe52F/f38tSyBZZJocYSao9GK1MiY5RBK6C96cyNLiqWbiKS3l\n+dxmQ6F0Kq7mlifEWqXWkwr7tMZ1bqp1pcSRLq58Nz0TYhJh1kCJ3snfoX/witX7nBN53C/S4rVU\nIWOA8Vrrsuvisd/vU1hVHQvnoVWBwqpgbJikm1ilX0EQYDgcwnXdtd3+NtGfKqInAFGuQp1Op7T+\nlC14s14Xy1w/veHXTif+tbpWhDdh8r/udR5aX+Jd7OayBUaXrZLIIvCAmhbb47tzn4398d35elnS\nn38gKzFlEkNpAmqx9/FJLEzMtm2ruCpiYp4Wr+W6LoIgsDZey0Z25bmTJB4prHaAHbnOy4DCqmBs\nFQzL9Csa47Ou25/tlHXOVN0vlQBEjTs5Zd3JYc/56lQkidpUJIQZ1E3X87KWKwlIb1G8LLSbiRXV\nLurSZ0qprtqE1rUguX0cutiKsxRFCxUnxVuZrFbhshiXQH0/iX31DcJ3WmjZVnFVNHHxWnoxYz1e\na5WU77tizdmFY4yDroC7gB0eQVWEwipn4lwBbXs4ZRUPemrvPGN8bBWgRaAnAOl0Ouh0OhBChGmZ\nyWYIRRUQLwhkYI6p0i/NNOEUeNMV4tqp6zxIEGFRcROum5JUYq4P2j50ERXdr9qmSWhlsUwpN0f1\n/yyJLLKIqmi7cB/TbfaufBn9w5uSt7OD6C6Ey8ZrVfmF2a6TNAdxHAfXXHNNwT0ihbKj86sioLAq\nGJvElE6akCk6tbdNwqrIvqgEIKa6XzaMiQ192AQ95+9nVioZEUzBLIZHS1YBrO/6B2jxRkGCgPLi\nLT5J4sqU+CFpH2nfRVO1p1mtEi1VEXfBqJj1I98v9C1JdAmERY9lQHGVkSzxWr7vh9YvXXBVHdte\neuZF0nFeuXKFWQGrTgWe47ZCYVUCanK6DTdv3e2v3W4Xmtq7ChP4rARBAMdx4Pt+KFzJIpsQdj3n\n72fWDrEoqub3lm2DuigJ3fk2mARC75fJzS/wFy1Oql9R61QccaJNxxsnx1uF20qoWbUsWWOuRB2o\nTdv3Lv81+mf+1fr7XoNtub/rxMVrKbGlx2sBU+8FpnyvJoyx2gXoCpgXFFY5Y3rg2PjW35SUQHf7\ni1pPiuiPLeR5vqSUGI1GGI1GaLfb6PV6scduy3VjQx9WpXfyd9MJv575DzgVK+ted6GoMGcDXGhn\nsiopV7o0F8Po9kzts4iqsK0mrozHkUKS1cqfaJYqPUPgBKGA1b8PPGQStsHkdN/hNmpWiKttR4/X\nUqiyGsqFUGUiXDVey0a2URSvApNX7Dbb/By3HQqrErBlgqyj90klTVDWk2azWfiDxqYxyqsvZQrX\nVdnmCcecqNJFgOmYpEQoiNIsOSbihFPUKuZPlncLTBNRaecoap1KsgpF463mxJche2JcLauF7Upt\nLLQaVlHXzNhjmMx/VslHtG33vv0X6L/olvRtkcwooSWlDLOTMl5r+0h7nlFY7QAZSnCQ1aCwKgGb\nRINCWayGw2Em60kR/bFtjDbFqvFqVR6TVVGTuegb8uhYhaIKMD9QlGtg1IIFzAuPLCJLP0dpiStU\nm1hxNQFqWl24BTe/iCiSPiC0banl0X7Huf4FPowWtqyY3BjVeGQWTUqcmYoGT6Kt5xHaOQTFVR5E\nLR2meC09C6EpXsvmlO+7YrEC4l+U9ft9xlhVHc4lcoPCKme2wRVQ+dF7nrdV1pOi2NT5iqapLzJe\nbZOUee2qFwB65kQhBMbjcfhWXE3aFL3LfzMTEfJUdIialqBhiTfpUSGTKrQSMv5FBVitYRZ9UXGl\nr5M5DiySqnwZTIks5pZHklNkSbm+EIc1E1FKOEW/BzKIqtpp8hEoV08fvW/9OfoveV3yumSjqN+i\nnvJdj9caj8ehC2HUqrWN98RtI0080mK1C9gzB60aFFYFEJ2Y2ySsdLe/Wq1mzc3UpjFSrPMm0/M8\nDAYDSClXTlNvw5jYMOkJggDHx8eo1+vo9Xrh2/CoOxIADIdD9Gr1SJIKD+HE2yQAljnGZaxZgTer\nV5VQwDc2I+Aku1tgrKtgikCKI/DNNaeyWO+WidVKEk7+rH5bbAyXC9RnCV+Ue6VyY6wBvW8+if7V\n35fehw0hpaTrm0ZcvFbUsmVDvNYuWazi8H0/t1IqxBLoCpgb/OWUgA0TZFOtpMFgUGqfTNjwkFtn\n/1JKDAYDuK6Lvb09tNvt0o9nW1Fvun3fR6/XQ6vVCidlUXckKSUcx8HVk69NRUBdZevzYib5m0in\n7icLp7BeVYIo0UVRWsrzIOIWqLfPnPzBsE2TIEiyQplITGQxxlxhY91F0/R/b5RN7PpanTe9bhcA\nCFG4uKoqm7onx9XXUlYtz/OM8VpKbJHVSTuH25x8hJCyobAqgTKFlcrqNBwO0Wg0cHR0hFqtBt/3\nSxd7Orbd1JdNka/GeTAYoNlshuO8iT6USRl90MeyXq+j1WplSkf/Mu85AGIqqkxiZq62knZulLtg\nNFFD1iQWWdqaklaoN4iBl1zTyRgbZVgnToilWtaCZHGlF+tV2/JGs23r8V16IguVBCOmyLWfsfh1\nVLCZ1tPjrOb+T/dm24mmfAcW47VGo1EoynTr1qaeGTa8zCuTsp8xpCB4nnODwqoAbHEF1N3Rut1u\n+JawzD4lsU31vnR834fjOJBSotfrzY0zWQ59LA8ODsLJVRoHx38DqDpVCwIjpc5SKAjEajFJwMx6\nFZxayuL2E5e0Imuih3UwCaS4NqsQLSKcZVnUauWrdOqG8fDGKWNUA6DFXEkfvW88gf5L71jyQEiZ\nMF5r82R5rnLsqg5dAfOCwqoETDWj8kRl+0tyR7NZWNlAlr6Y3CvzeDhto9hcFr2+lz6Wvp8+0e9d\n/mtMM/xFMuT5nllAZHVxC0VGTJY/0/Xhe1NxFXftJGYE1ATPXKILwxjIYBqLHFrYgtO2poyApn3N\nfY65P3mj+UQagb/oglhrmOOlJgOz0JwMI4WHZ+LKd2F0Z9QFVxzKUqWP78wSV4S4qvJvtOz4saR4\nrWjK91XitWx55uRJ0vWpRCqpODtwnZcFfz0lUJRgUFnojo+PAQBHR0epk/1deKjkgeu6OD4+hu/7\nODo6wt7e3sYnVjZM1Iq4dieTCa5cuQLP83B4eLjUWPb++cLpZD+MVZJTgaOTKqbSakF5078sLmy+\nl1yoN/AWA4mlJoyM6yzxfeCvZnmKc9tbhmicWNyyaP/CcdWuNXXd6aIq7lr0x6f99yeR8Q/QfeGx\npF6TLUO5BrZaLXQ6HXS7XXS73bCUhed5GA6HGAwG4UtGz/Ni72U23GvLot/vY39/v+xukLyRsrp/\nBslmyYsAACAASURBVIQQPySE+LIQ4hkhxC/GtPmt2fK/EEK8dvbdK4UQT2l/x0KI9yQNLS1WBVCG\ndcjzPDiOAwCZstDZ+CDZBotVEARwHCcsppwl9oeY0S2ry9T3UvT++cLUvUytE81It461KkSf6M/E\njxIBc/WmTGnTk1Kqp1iujBkBk2pRpQlDQwr3uLTuSeuqbH163yfDeBdIZcFTeOOYfejHpqVcT7NU\n+YbtKeuVEKElTog6ui88BueaNyRvj2wtq8ZrVdnaqEg6xpOTE2uyA5M82R1XQCFEHcADAO4EcAnA\nF4QQD0spn9ba3A3gBinljUKIOwB8AMDrpZR/C0CJrNps/T9M2h+FVUnkJRjWmZzaFtNkk7CKoruq\nFVlM2bZztAmklJhMJnAcB61WKzHRR+I1IeqL7n9RVLa8umH7esruVQhcoGZaP1KvKim2K05c6X0L\nIpaehaQVk8V+pAmpuFTncyJqRQuW9BcthsCpqBKRBCFxYkttKxqbpUSTSVQp5goHz2KvZIDuP/5/\ncL7r32Y9EoLtdnPMGq+l3PV3MV6LNax2BEvnVjnxfQCelVI+BwBCiI8B+GEAT2ttzgP4EABIKZ8Q\nQpwRQlwjpXxBa3MngK9IKS8m7YzCqgTyEAzR4rOrZKGzTcjY1B+9L5PJBIPBYCeLKW/6nOh11NZJ\n9NH71p9PJ89CzE++RV1zA9P6rSwf0cmSSTzU2xl6oFKpz9ZPEndJqchNwivJjTAOXeQp0ZTFIqXa\npLkBRrcVFYVRy5RO0rK5fUQscknCKWtKdk1giVodMgDF1Q5jitcaDoehkDLFa+lZCLdVbNFiRXZM\nWJ0FoIuh5wFEA21Nbc4B0IXVPQD+W9rOKKwKwOQKuEk2NdG3ScjYhnqD2e/3MZlMVnJV21Q/qnCO\n9BcBnU5nLYvf4bef0gRVJN23mI2V0Q0w4/70CX0Wi5aUgEwRMboFKuoaGGc5811zJr1lLG1Ry5TJ\nUpWlDbAodFQB5ChRy1QUXQhPBuZ2unCKWq2SBNfcbmZiUQkrTdx1L/2/cM7+u0zbybSvLbbqEKBe\nr8+5EepWLVXIGIAxOcY2kJSAhBarXWF3XAEx91Y1kegPOFxPCNEC8GYAxvgsHQqrEtjU5DgIAgwG\nA3ieh/39fTSbzbVu7LZN2m3pj8o4NRgM0Gq1cObMma15gNqIiv/bhMWv809PzJIgiPlkFXkVAlaT\n8yxCJs5CpCxQSYIobllcmnJT+9DqlHLM/gSop1iyVvkdJlmmXCch1bx2jNHMiAsp13XBZU5RL/3J\nvHidWa2k7wGQs32wJEJWdlE0RuO1lAuhitdyXTd0IcyrvlZRUFjtCBbMrTbF577wJfzpF76U1OQS\ngOu0z9dhapFKanNu9p3iTQD+XEr5zbT+UFiVwLqCIRrfc3R0tJGbty1CRmFDf1TtryAI0G63S8+W\nVPaYrLN/PR39qhY/ff+t5/90PlkFMLNSRYRH1sK+y6CsMPUmEl+GeSOgkeBK6LvJcVVGt0Dv1D1R\ntyb5rsG1cbJ83FgoHhNc/YzrqUQW2v70eKm0ulZxLo+mmCvpJ9a4kt54fuxEzSiupv2tA4GP7vOP\nwjl3p7kPZGfIWuNJuRDq8Vp6cgzP88LU5cumfM+bNFfAw8PDgntECseURGlLeeNtN+GNt90Ufv6P\nv/MH0SZfBHCjEOJ6AF8H8FYAPx5p8zCA+wF8TAjxegCXI/FVPw7go1n6Q2FVAHFZAVd58+e6LgaD\nAer1+s7F9xSJlBKDwSCs/TWZTDjWa6Cu20ajsVL8X5Tm1x4FGp159z+TqIojOolPs9jE4U+mfVDi\nKc4VLklc6ctXiadaBiVGosebxWqli6swE2Ka2DJsVwmwxALJMxHmR9wIY6xSp+stW1hZQBfG3Yuf\ngXPdXUusT8gUZa2q1+thrGhcfa2oVcumulEnJyf4ru/6rrK7QXLHnpfoeSOl9IQQ9wP4DIA6gA9K\nKZ8WQtw3W/6glPIRIcTdQohnATgA3qXWF0J0MU1c8VNZ9kdhVQKrvK3Sg/zzSutdtjUkShn9kVKG\nIqDZbIYiwPd9K8bGlnOU9aWA7q7a7XZXTk6xgKghrFU1K/w6v1yPwVEJJfT+Rtqb0njHCY1VxRMQ\nX6w3bv3YeCslOCLHYdqOaRtK8CSlL8/SxkRsdkQgtq5VVEClEcZVzY5fE1RSjXU0SUiq1Wr6302I\nqyq7y1X52IDNHp8utvTt6/Favu+H1q+i4rWSjrHf76PX6+W2b0LKQEr5KQCfinz3YOTz/THrOgBe\nknVfFFYlkTVttu4+tW6Qf9Y+2ULR/fF9H47jQEppzFBn09iURdZrT09OsUl3VQB48eUvzjK6+RCo\nnYoqPVlF+O8a+4yz7ujoQsEbzwsYU1HeJAHmjeeFVzQWK2rN8ifz21o2HXpUMPkTLLzFjLaJ9kFZ\nnUwJJLzR6TbUGHqjeStVktXK0xJZaG6E0hvFXkuhqIo773NiURNZUmrp+uvofu1P4PyLf2/eBiFr\nEBevpcRWEfFaacKKroA7AOczuUFhVQCmG1iaaFC1fTbpPpWGbcIKKEbMRMVrp9PJPZPjqth4jqLo\nAjVLcepl2P/Hz08TDwQ+RDTdt55iPZElf0dqEp4l7bqa2Gd1/dMJvPh4MFO8Vdr2/Uj81bqJOxRR\n33yT+2JSuvaF1OwZ47DMG4M6n9IbYeEYTantTRY4lVVSUWtQXO0oRVvkTCnfy4zXYvKKHaFCMVa2\nQWFVEkkTZH1iulH3qTX6VAZFPNz0mLWVC9PuGHHWVl2g7u3tod1ub/QcNp/77EKyChlMIJBhIr5W\nP2YPIFNyBh39+vDGyfFHccvTXAqzto8mbwCm/dfFYfQzsOg2mORGmNivSFIOFYtmwmS1MlnApA85\nE3Gpk99orJWx6PCsULCOsloFAd/oxlB1V0AbyDteK81iRWG1A1BY5QaFVUmYJupBEGA4HIYJEzY9\nMc2CTeIhTzETBAEcx8k1Zi0PbBV4k8kEjuOkCtRVaX7l/wEa++FkWdSaU1FVS7BS6b+dqJUiU9Ff\nA1KeTvrTthEVDFkTU0RdAhW6ENKPJ839LYm5bc62k0VcRbdhEolJbn5JLoQ6mSxYwTSl+nQFLFit\nvCEyWSnnYq5qQAB0n/tjONf/D+nrkkpg471VYYrX0q1aWeO10o6x3+/j6Ogot+MglkBhlRv2pKKp\nMGmugCoe5fj4GABwdHRkdEcro59lkoeIUFaV4+PjUARkEVW2CpqyUUWTHcfB/v4+Dg4O8nFZrTVO\nhUngQcYVrVVWkcCdig/1F8UfL/4tizfI0GYUvyxpn1ELizreuHVMadZNVhrT+sscu9pmWuyVAZnU\nRlsmXce8vjc2xq1JozUK8yI4ltm1qh9PpJ/dr34yZRumXVfTqrMr98BtOXcq3Xu73cbe3h663S72\n9vbQaDTCREyO42AwGGA0GoXiC4g/xpOTk41brD796U/jpptuwo033oj3vve9xjbvec97cOONN+KW\nW27BU089FX5/+fJlvOUtb8HNN9+MV73qVXj88cc32redJZDV/SsZWqwKIjoxV59VsVQAG49HWZaq\niwcVs7aJwrRlYcM5EkKEGa1U0eRNJqeI0vzqpwDUpu5nmhVE1OqzIq+AaNQhfXdqwYrG92Ttlz4J\nD61RKW/1TO50CjVBjyZsMK1vEh2xmQLHMGY1THLPiya2iAqOhc/R9kskxvC0trPzJQ0CR7oOREwB\nYel7p8ukH57nuTa6eJmLpZpZrfyxdu5PY7EWUKJK77f6bmYt6371k3D+5Q+b199BtkV4LMu2C+Is\n8VpKWCkX+Fqthu985zt4yUteglqtFsYabwrf93H//ffj0UcfxdmzZ3H77bfj/PnzuPnmm8M2jzzy\nCJ599lk888wzeOKJJ/Dud787FFA/+7M/i7vvvhuf+MQn5uZLZE1oscoNCqsSGY/Hc65oZd/QbZi0\n62yqPyrl92QyCWPW1ilMu+uoGl95JKeI0vzqp07Tqeviw5+cng8hIBcm/mtazUJ3P02sxJ1/fzzt\nYyNhMhJ1i9PjjfzxkgkbYjCJK5Ob4CrWubj96cIzQxFhGXgQCe6BJgGVuL04a1XYIKGuVXQcdFdA\n9X9lKZQS3Wc/AeeGtyzVP0LKJhqvpZ6H7XY7TIzxjne8A08//TRe+9rXwvM8PPLII7jjjjvw0pe+\ndO39P/nkk7jhhhtw/fXXAwDuuecefPKTn5wTVg8//DDe+c53AgDuuOMOXL58GS+88AI6nQ4+//nP\n40Mf+hAAhIm8yAagsMoNugIWjJQSo9EoDDw9OjoqJZbKhG3iYd3+qLE+Pj6GEAJnzpxZWcDaNDZl\n9UO5UUop0Wg0cHh4mK+oevbhmahqnAqRWiO2rpKIy6i3Dp47b8lIbJvg9if9ZEETt8wbn07uw7aT\n+famNOxpGFOtp/QpiyBbssBxkpBSy+RkNL/dsPbXcF6g6hMFY1/Tlitmj0Uh5hOA1Jvo/u3HE9ar\nPttu0Umj6scHTI9RxV61Wi3s7e3hM5/5DB5//HHce++9GA6HeP/7349XvvKVuP766/HWt74V73vf\n+/Dkk0+utL9Lly7huuuuCz+fO3cOly5dSm3z/PPP46tf/SquvvpqvOtd78Ktt96Kn/qpn8JgkMEF\nm6Qjg+r+lQyFVUEIITCZTHDlyhW4rot2u41ms2lVxXWbxMO6eJ4XjvXBwQG63W4lHphlHYMaz8lk\nglqtVoyFVWUADAsBe6cCIMUyoli0ZK2I587SeYcbjmmXIK6AbOIqKk7ihJ0xXsogkJJSn8etG9fP\nyLZkZH9ysnj8UTdAGXhGS9OCgFoVbzxvXYze05LOUXhNRwoLi9p0Oxnch6tyDyW7xbXXXos3v/nN\nODg4wGc/+1n88z//Mz772c/izW9+M772ta/hD/7gD1ba7jK1D6PreZ6HCxcu4Gd+5mdw4cIFdLtd\n/Oqv/upK/SARpKzuX8nQFbAg+v1+mO2v1WqFboAknlWEnnJTc113oy6WVRKdy2AazytXruS+3+Yz\nfzgTVrNbVNyEW892FU7yI2ngY7LmiaRMd4DxBi29EUSSyx+QHFMFLGbRm7PGxByn5wINQ38NboTS\nH0MspFE3ZBTMkjY9IYbMFDe1CnPxVNFlrnN6fLqroeucFoZepvaVElVJLoI6UffGWgPdL38Uzk0/\nnrpqFV7kkOqRZJXTn3G1Wg2veMUr8IpXvAI/8RM/sfL+zp49i4sXL4afL168iHPnziW2ef7553H2\n7FlIKXHu3DncfvvtAIC3vOUtFFabwgLLTlWxx1xScTqdzpzbn40Tddv6tEx/VGbFy5cvA4BVLpab\npMhz5LruXKbKosYzFFVR1HdRURJ4Kz0kpO9O/9LidABIzUIloxaPYHHfSaIjMTtenCUsT+YsVYYs\nitGsiWlWK81KKP2xwQJn+E5nHavVRHMTWrBUpVju1HEG7uz/SoC6M2vpbP1GE90vf3T1Pm4xVXeV\nq/rxAcnHOB6P0W6vWIoihttuuw3PPPMMnnvuObiui49//OM4f/78XJvz58/jwx/+MADg8ccfx5kz\nZ3DNNdfgZS97Ga677jr83d/9HQDg0Ucfxatf/eqN9m9nKdtdr8KugLRYFUSz2ZyzUNkmYgD7+pS1\nP3pB5V6vl0tBZdvGJk/0Gl+mAtV5jkXzbz8x/U/dYKUIJ9zajTOrpSJusqRKHmjiSmQo0KvaJ7UN\nLUcGsZRk+ZqzOOkiw3MXjkOJGNHYC9dd2IYiFEfa+zRjPFaGB5PBvdDkBpgVOe5nc+9UQho4TWoC\nTMdYHYvJguWNsPAeMavVStROH9a+O03nKwN0/+bDcF79k+nrE7Il5JFqvdFo4IEHHsBdd90F3/dx\n77334uabb8aDDz4IALjvvvtw991345FHHsENN9yAbreLhx56KFz//e9/P97+9rfDdV18z/d8z9wy\nQmyEwqokbJyo29gnIP4Nm0qmMB6Pcy+obMtbTJXqPA+U1W84HKLdbqPX6xV/3LX6dFKsBJWabJuu\nS6OoWr+/oWiKcxXU3ohJbwxRmxeec9YtfxybBU96o4VlypplFEZqfxmEX7iNhfOX7qQg/QlEioug\nnIzmUsGbrFaprpZpBYTVOC7j6rfQUZkeY2ayLuoZAhV6LTVgmszir34fzmv+x9X6Rqxj1y1W/X4f\nvV5v4/t805vehDe96U1z3913331znx944AHjurfccgu+8IUvbLxPO4+Fc72qQGFVIjaKGMCeh0tS\nH1zXxWAwCNOvFpEExNbztQlUfZCsNb7yGIvmM384zfgm5KKVKnQDNJxnkcO5lz6kNwwtQfHtglgR\nFDbRxFDUDTAxZmsJl7hMfcWiYFMWrrT+A9ksedF9hSgRZXK7VK6VGdK1h23D62NmtVLfq+vEKMYC\nLAhLb7S81aomADRi+2vL/TMPqnxsu0LSvTsPixWxFAtc5qoKhVVBRB9GNlqH9NgvWx6e0f74vo/B\nYDBX/6vIfpTNpvuxitUvj2uj+eX/6zT7miLNoqHEX1zmv2g/E8RDHNIbTt/spYiKZcTV4jKzuJLS\nhzBYauK2Jb3hgsg0tU3r67RNutVqroCxN5z+W9N+j74L6FYrk1CME49KlIUWyxWtVmG/DOumJd9Q\nVit3CLT2Tvuj+jzrW/cvPwjnX9+7fN+Iddj07MuTuGOksNohKKxyg8KqJHbh5r1JVE2q0WiETqdT\njptaxZhMJnAcp1Crn4lQVMlg+m8tYg2Im1CribEx0YXh2tAn0suKLCUiEh5GMprtDzituYSZ5Sem\n1pYxoYXvQkKPn9KSQnjjxWP0J/MCcIlU80psJSbdmIm0dWKpUkkS03rSkIUMgQZLlRJV8zsAUJsu\nUyI0KdbKHc7/q86/DKbntt6cugRSXJEtQdWxMtHv93F4eFhwj0gpUFjlBrMCFsQ2WKwA+/ql1/+a\nTCY4PDzE3t5e4aLKlnHZRD+CIEC/34fjONjf30ev11tKVG18LFRWPyWo4qwYKkGBHs+zauyNP55O\n1JdJGe6N0+tUpWUY9CLucab/r4OpPpSnElqcjpv0x4v1pRY+TxYyJi5kUIx+VvFMalu6uDMJHdN4\nxp2TZTMm6hOHwLBu0sTCHU3/om6m+udafXotBt5UXD31geX6t4VU3aJT9eNLgxarHaLsWlOsY0U2\njZqc2nYjt0VAAFMBoOooqex0ZY+VbedrGaSUYWxau93G0dFR6cfS/NJ/m4+nUv+fS6k+m5yvKqLS\n8GcFZZU7XtoE3htN28ZNzHUXOZ008eQNAUOc1NTFL8aVLaPlbWrhyuk9WlQwJSWLCNx5d0Eg3eWz\n1ogXtGrfgT9vtTJmO5wxcRbHQrdauRkscnrMlernzO3RlvsnISaSnmEUVjsELVa5QYtVSZQ9oY3D\nBmGl3P5UDaVer7exQr+rYsv5WvX8+L6Pk5MTjEYjHBwcYH9/v/Rjav7FQ4CpSLYuQEwiJ63fqx6X\nN1qcwMeNdRbLlclKEi6LKwRscl8z7C9JvHjjdMuZapf0GTDXtMqbJBdG/XrIYuWLWq0mw/jlADAe\nLH6XZrUKXQoDdC/8l2kTS+4XZDm2+cVZVpKeH47jUFjtCmXXmqpwHSsKq4Iw3axtEDFRyu6T53m4\ncuUKXNfFwcFBana6Iil7bFZBJae4cuUKWq0WDg8P0WisZ6jexDg0/+r/nFoimu35ibSaLPvu/Pdp\n1qokC4UJvf/RY8nqipYWw5QkvqKiK9CL9LrZ46NCl7vI8a8sLjMIp6ioi+47WojXd+cFo1o/GjMF\nxAtLE3HnKSqeFK72venhO+pn3zcwf5z+ZCqy6k0c/uV/XW47W8QuCI9dIMlixRirHaFsdz26ApI8\nsHWiXkaflMuf67phtj89SyGZssx4qOQU9Xo9Uwr1UohmjgPSXdbURF4IAMpqUUsWV42s2SNVIViV\nlS5lPd19z2ShUm6DC7uZxZKZXAbjMuDFbcsfY+EdWdRNUB1P1NUwzm1RLQOm4xqXIXBVC1ZqbSnt\nunAjxYP18VEJT4B5d0DdvVBv4/un2STD7QXzoiu6DnDq+hcVbaZEHlLi6i/9Hk5uvT+8h5HtYBeE\nY1odK1qsdoSc6mESWqxKxUbRUPRDRRWlvXz5MgDg6OhoIeW3LWNk4/kyEQQBHMdBv98Pk1PYJKqa\nf/HQ9D+12TmOs9DoGfRUm1WTPHiu2dUvdb0M7dOsLN5o+X7HCZZl+7+w/qyvSZYpkyuhP5nvU5rV\nKu2z6Tjck/g+RcdvHWuVQlmtxs7idwvrO+Zt6+JLJVaZJWI5ePLXMRgMMBwO4bouPM/bivsH2V2Y\nFXCHKNtdr2BXQCHEDwkhviyEeEYI8YsxbX5rtvwvhBCv1b4/I4T4hBDiaSHEl4QQr08aWlqsCoKu\ngIv4vg/HcSClRK/XQ7O5+Fa86m8PlyXp/OjJKVqtVm4p1Ne5Rpp//jtAqzuzKDQBbwI0motWK0Cz\nTKUdQ5Zj1G62alKflvhBvdGLsxTproHeMN26ZcIbm4se60RFSZyoiR5PXHILb4i5Mcvi/mfC1A/T\ndbGqGPTdeKGjE2eRirNa6ShRFbccmIoqE6rOFTCfzEL9v9HE3t4efN9HEARwXRdBEKBWq6FWq6Fe\nr6Ner2+VVavqFp2qHx+QfIx0BdwhLIhFKgoxLQj5AIA7AVwC8AUhxMNSyqe1NncDuEFKeaMQ4g4A\nHwCgBNRvAnhESvkWIUQDQDdpf7RYlciuCivl9qfH/ZhEVVH9yYpNfYni+z76/T5GoxF6vR663W5p\ndakSqTdnLnCaqNIJvGwxRpuY/KiU61nwBhnaGGKGTMuS1tPXXdVqpQsef7yau16WddIEWTQ1fppA\nBJIte2rZZGC+PkxWKdP3esIU0+9ZTThcJ15U6ShBJmrzVlYpcfDE+9BsNtFut7G/v49ut4t2u41a\nrQbf9zEcDuE4Tlikm1Ytkidp1xZdAUlF+T4Az0opn5NSTgB8DMAPR9qcB/AhAJBSPgHgjBDiGiHE\nEYAfkFL+/myZJ6U8TtqZhTOv6rINtazy7pPrujg+PkYQBDg6OkKn00l8Q2jbGNnUFwBzySkajUai\nSC2b5n//4Okk1NMm2Z4hNsqUfjuvdOFZhUeSSNGtW3GoZSbxELfeMuIq83EYxnsTQiorpr7HuVMu\nUeT4dB1NOA2vnP4/+oZ2HBHL+vI4l8IocZkUlchqtNB9/H3hIiEE6vU6Wq0WOp0Out1uWEoCOI2L\ndBwHo9EIruvC933r7jtVZRcsVkC8JwizAu4QZSeYKDZ5xVkAF7XPz8++S2tzDsC/BPBNIcRDQogL\nQojfFULsJw0thVWJ2CYagPz6pNJ9DwaDlYrS2oAND1z9/KgMikUXTl7lGml+8QOnE3r1r7Ja1RrA\nZDz9i6JPrJUly3dP44C88ang0cXBslYaf5zNKqXaJtW6irNAmZZtGtNxGyf/GcZK/z6L8DEVXI6u\nlyV7Y5ghMGWs9H2PEuKzTOiCy0SW61slrpgMp2Os/gXmr2UZoPtnvxq7GSEEGo0G2u029vb20O12\n0el0UK/XEQQBxuMxHMfBYDDAeDzGZDIJa/wVza4Ij6qSdv6klFbF45IcKTsOqtgYq6w3y+iPQ2Ia\nMnUrgP8ipbwVgAPgf0naCGOsCiQ6IbVRWAGbtcqomlSj0QidTge9Xm+pB7NNY2RLX6SUcBxnIYOi\nrTT//HemrnuN9mmGOdMEO+6BribYWaxYUcFQb2MuvioNFU+VljEpLu4qXG4u9pu4zBstHmM0fiqI\nCJlNFk3OUnA4KYvgKqRlB4wyPF50H40japGKQ8p511JTpj+d6PJosWBgGjfnTWZur63FFPQJKKtW\nvV4PLVlSyjBWy/M8uK47281prFatVrP6PvD/s/f20dZcdZngs+ucc8+999yPN8pA9E2QduV1kaCQ\ntAQYB1tAIyQ2rygsAmtYsJSPLCTSupzGNUwzbauDjTatYAYmji0Lhu4JvaSVyASY5ktpnARZRtQR\nx2QkdhLGtB/J/Tjn1Nfee/6o2lW7du2vOvd81D2nnrXOet9btatqn111qvZTz+/3/Dq0G5zzVjzf\nOiwJa5Rj9fk//iv87h//Z1uTRwFcLf19NTJFytbmqnwZAfAI5/wP8uW/iY5YtRdtmajLmOeDOUkS\nTCYTBEEws903IQSsswUtkCTZRJtzvjBzCh80um7FZFxVrEygtAznEs6BOlLlAxqVDxCVEJi+Qxpm\n6wqSYbj+jFbqDWtq+ezTh/SIdkC5D6Gg6AiRbp+q4uSjgKmW+TWrd2l9kpMduS8mm3rT/tVji1BS\n2axCDgeU7eJly3S5vUA8sYec2kiXIFiyqUXQz0gV5xh98V9i/N9Yn8fmXeeqloCYBAuyFUXRuTfG\naAPWXZHz+X7r/P07SFgjYvWC77gaL/iOkhP97L/7otrkywAuEUKeBuDrAG4F8Gqlzd0AbgdwV+76\n9wTn/DEAIIQ8TAj5Ns75XyAzwPi/bf3piNUK0UbSMA+yxxjDZDJBmqbY3d3FYDBYi5v1KomwsFCn\n+YRxNBqtbEybHHfw5fdnk2hGgZ40YRUTXXliK8KnZiVRLqQ5yRpo1CJdaJ+XghOa3QDTaeZ8KEOQ\nLqFaNVFsdG1dypmKmg26R8ikzwNYlwvlW+w3ibJC0S4IBz+d6YmKeNzsOuK8ThibKFkFqZLUqyCo\nKp8sPRO5qhwuJ0zyixXOORhjoJSCUoo4jovQLpVszYp1Jh5te8m5CLi+47qe2w4abMD1LsA5Twkh\ntwP4FIAegH/DOf8qIeS2fP2dnPN7CCG3EEIeRBbu9yPSLn4cwL8lhGwB+H+VdTV0xGqJWHfzClGT\najqdYjgc4vDw8Mw36jaO0TKhjune3h4ef/zxVXfLC4P/619nCfxBvwz/0xWapbFeJQgc186sZhbJ\nVE+udKCRuTiugC3sjyV1ciVvFzQoBKxO9G3ttcui+pj5EDOfNvG0So5qypdFdfKBycQimlTPXivd\nUAAAIABJREFUj6xCVRSs/NqLc8VMjKNOtdJZr7uULBVpXBalFsfubQE0xuj3fg7jf/QO/315Qg4h\nFGCMFWQrSRKEYVi0E2SrCyGsYt3HwvT9KKXnLu+5wxmwRoqVDzjnnwDwCWXZncrftxu2/QqAG32P\n1RGrFaKNpGHWPqVpivF4DEII9vf3K2Erq+jPIrDsvqRpiskkmwjOc0znAdc4VEgVUA/HElAnzC6V\nIZ4CW56kSD2W6vrGGTDQmPuo300lYlpXPwO5YmmeZ2PKtzLkLOnyp8RYifaukMo0RD0X1wERgmfN\nH/Noo0Mi5TyJ7y3yoGTVKhq7FSxZtTIRdhWxJedK2KrXSBb3dwhMIuUa06iBedjj6HP/I8Yv/Fm/\n/Z4BIjRQ3DuEqiXIVpqmRQihmqu17gRjE+GqYbW3t7fkHnVYGTaMWC0T7ZmpbSDaRBoEmvZJ1KRa\npJFCW8ZoWedLWKhHUYSdnR0Mh8PKmIp+tDoUUOTN6MwYgl42sXZNhsXElAQAJBIh6hLJCkITsgWU\nDxVdzo+2Lx4qly23yqZqFdtbaji5kIZ1NSuN6uQnmdTJ5LxUKxniHMkESQ35s9m3q23D0+xf+TyZ\nzCmmT5TXVkW1klQzWf3T1aoSqlU8Lq8zUxFhU/0sOdeKJlKI4Opc11zGGMJxENAbY6x7KOC6fjcf\nnJ6edsRqk9CSedU6oiNWS8R5CAX0BecccRxjMplga2trYUYKm/agE3Vs+v3+Ss0pzoLBF38pr+Hj\ncAEUkCerYrLd9LxHyuR4aC2MXgXjQBwCWzojConsJFM7GdSFlVXWqwVyha24QbXSkSBbexeaWL0L\nIpVYVB7RRhAL31wpE86yvUu1shX6ZbQkO76hgQLRuLpO6xDYL8910MuOxyhGn/1nGL/o5839WhKa\nGGMIV0KhaG3a/fm8w0YeT09PcXBwsOQedVgZOsVqYeiI1QrRRmLl0ydKKcbjMTjn2NvbW2hB2jaN\n0SL7ohp+bG2Z81FWPSa24w9+7xfKybFMqgqzCl1O0QymFfJkVveAEESriZJlIlcy1Am86mhnC1W0\nrUsj/djYyFUtD0jTf53SJPYpEy1t0d7Q/rdpmQ4q8QUyxUkliHI7QbSEWqVCR6YiQ9tiGyXXyxYe\nGJ3WCb5MsnTfSYWsWqmki7PWkCsZNmOMMAzBGMN0Op27McaqsQmKle25cXx83BUH3iR0xGph6IjV\nitEW0iBgmzS7QtSW3Z91gE75W4uHu5h8mpQqzsvaPrbvO6tBBZA9OMTk11fBEpN4W/toAgwthdcF\ngdKF9jXNERNQc9Hiqf93MpGrs4ytCbo8I1c4oE19U/OURHsbIQKqpCs8doffyaoVUN+/qlrJpEpd\n56NaFcdNMfqPP43xTe+y92/FECGEADAcDgv1ymSMIQhXZ4zRPtgUq45YbRA6YrUwdMRqiTgPoYCi\nj+rbOzH5P88hamfFvO3xZeWviTlFG68bIA8BHEjW6j6mArqH/CImYgVh2vV7oERjPXERNZOiST1s\nLVXywEyW4Lp1gkAIwibnHyUTvZon91FsL1QrNX/JR1lSCWM0qStgqioWTdy5ZzoTBxNkNz0fyNfY\n9KhZ/lJ4om8/PQZ6lt+ij1IFZPbsOvMURrM+i7BDXR2vcwCXMYbI11Jztdr67NgUxco0/h2x2jC0\ncA6xLmjnHW5DIJOYNkGeuFNKcXJygslkgtFohL29vaU+GNtEIub10BXK3/HxMQaDAQ4ODlrl+OeC\n7pwMPv/zAE3LSaM84ZWNBNLIblqwaEQTs+lBra1jAu0iDL4T8Mo2hr412VesIVG6ZT7joNtOheqa\np/6tqj9JVD22uB50KpRu2cSz3ICslsrkhcZlyKC8XEdw1HtPNLFPSOJJ9hE1r1QlS9e3oIfRf/xp\n8z5bBBv5EGrVYDDA9vY2dnd3MRqNCkMjUTB+PB5jOp0ijmNQSltzf990dMSqQ4f54PzM5tYQbX07\nJpSZKIoQhiG2t7ext7e3kv62iVgBZyfBYnIRBAEODg4qNWeW2Y+5QyTl9/rVSaMgWHIOka6eEU3K\n7UyTUR22LCF5Ngh1hjnG0Rb2x1IgSv1C8lIlJNKkiAHNiKdtPzaYCJPt+4ptbLloNpMIG+TvPItq\nJa4dV0ifC4Lw0bSuWoWn5uvRZnChQvxWgNyOPzez+MRPYXzzu5v1t+VoYowh52utwhhjUxQrm936\nxYsXl9yjDitDFwq4MHSK1RKhu6G1jTgA2c339PQUaZri4OAAOzs7K3/gtGGMznKuGGMYj8c4PT0t\niOqspGrV50LF4LM/k00OB8Myb0qoVsJaXQca2xUsn4mqUAcShShUQrAM50xVbEx25y5lJxrXiZPI\nidKtk7fTgSrKiVDGRHvV3ttkDKHCplrZvuM8VKtUyRFrQh51eXq+26ca1SqaZMRJXW4C5/Xx0V1T\nJhKne1EQ9OrXd7+P0cffau/LOYcwxRgMBhgOh4WqJfJ1KaWYTqcVVStN01bc/9cBtnHsFKsNA+fr\n+1kxOsVqxWgTsRLOdJxzbG9vY3t7e+WT+FUf/6zgnBcW6vO0pW+LK+Dgsz9T5v8IpUGdRANVFUFM\nunX5LWcxVJDJlUnxUN/SCYVly6H6RBO3nbdpH6oTnQqdQUMKvXKkq5mURsCWdCv3LWgroJIGH1IW\nh/Wx9D2uKeRPNrFIY4P5h4cCJVQr35BPAdFeXJc61cqkTKnE3gbZsEMOmVXVtpZhUfcc2fBCQM7V\niuMYjLGFG2NsgmIFmJ+pJycnnd36JsEVrdFhZnTEasVoA7HinCOKIkynUwyHQ/R6PfT7/dY8ZNpS\nmLLpuaKUYjKZgFI6V1v6VY+DwODT78j+E/RLwwkdqRJI4/mTKRPERHfgWdQ2HrtrQ8UTe+ihjVzJ\n62SHv2jczGa+SciZCOuTSZGP+jQvJNPq28OmIX4ybEYowpjEpwaWTLZ0xEm7TU6+1XHneZHh2MNh\nUZApQT51RIxSoNfD6Hd+HOOX/qq7XyvCMu4/LmOMOI4LI4bzYIzRFrjqWHWK1QahCwVcGLq70BLR\nxlDANE1xfHyMOI6xv7+P3d1dBEGwcrInY9Vj1BScc4RhiOPj48JFcZG1vlaK/rBuBS4mz3K4lUq4\nlvVm3qYk1NQrNTRQEyIm2pjCBnWwFUfWHVcgmvg76plym5qqNgKu0D7dMh81Sb4Oas6Fju+qjqOt\n/eRIamcwsZAxPda30YVZyteN+M62SUpBpqTxkp8FNAFS6Xrq9TH6nR83728DoRpjjEajuRtjtOHl\n3SrREasNw6rD9bpQwA7zgkoSVkUaRJHHOI6LgrTioXLeiMyy4DMuaZpiPB6DEHImc4qz9mORIITg\nSff9y0xpoXFOrgyKQhL5qQJANlEW1t3y/5tCtbgWE1rb/sRk2qVKiTYm5SUem5UV27omSEK9EmdT\nzCrbT6tj4TM+6nazmlSohDSNDAQ237+sIuoIqlw8WK2R5Qub46IcnqeqhbFByZLhCo+Ua16RIFOt\nGAU4w+hjP4bxD77P3f8loW3E4zwZY7QFLsWqCwXcIHSK1cLQEasVY9mTZF1BWl34RJuI1aqJhE8/\n5OLJKlFdN2x/5p9Vw//kCW8amUmHqlLFISBfe4SUE1ESmCelsxKuZOoO9wPq+T5AfVJvI2C2dSYC\nKrZRVRh1X0LxEeRKbd80v0oHWWFpQrbkfgGlmiOvdxUEtq1Pk3r9L914ymRL3lbnHFgxsUjLsExG\n7YpYdGqvt6YjXWrhYELKt6u9AKBqUeEeRv/hjRj/8P9qPk6HAoIwyc8zEUJIKUWapkUIoRw+KMjW\nusP1DO2I1YahBXOqdUVHrFaMZZIGuSCtLeenbQ+ZthArE5ZdPHnl4yEUht6gnDgKS/XeVqYc6EL9\n5LC2M5lU5BN/zvwUGgFGy8m+S5VyEQAZOiXFRK7SqEoE5NC4eKIfN9O+krA+uVfbirES42QjTSYi\nJZM1U5umtuY2yGpYk/MAVK8xnwLVpjGX4WvhLhStpmqeqlqJn0bLzSzOA5oYYwBAr9cDpXTuxhht\ngul7xXGM4XAGxbfD+USnWC0MHbFaMlYRCiirKTs7O4W1rW8fO2RQx0W4KKZpitFotL55VBIGn3xb\nNtnrDfK6Vfks0PR2X9S2ksmWi1T5kC7xUJAnsU1IVnRqJ1csBeJUv08Rzha7nAIN66NTYLjn39dF\nwpVL5ZNbVftbCVUUZEycK5ksiRwwVwifaCerVkXNKR8CNa46M8qkpfL/XLWKDaYiusmIHCKokio1\nfFBVrZI4zwvIl3Fehs7m9a5GH30Dxi//dfv3WwLaFgo4K0zGGCJ0MAzDtTTG8Dl/63B+O3iim+Mt\nDB2xWjEWTWJmUVPaRqza1h/VRfHw8HCpD6RVjcfg4/8km+zJBU5FrSobTAqWjHmMXzzOHha+RYO9\n8qnGdqt0n0m9DtGpfr+mPsUTf/dA3T50+Vezhg1GE3OBYLkPsx5LzZVqUvNKPV/y+VFt710qmxoa\nGPSqDoDCFVDdn+tajjXfRyZcNC1fSOS/my4kcHEQqhYhBIPBAP1+v5KrlSQJKKVFOzlna12ISJue\nrx2WhE6xWhg6YrViEELA2PwvcNnqu6masqg+zYq2ECvRj5OTE3DOsb+/X0meXmcMfvstwNawNKrQ\nhWeJSStLS1XHRgYW9Qa4yO3xsFqPJ9kkdlYbdbEPsX2TXCwVgkCY8q1UFGF++f5dtZTisVsN1Blj\nmMwyrPtxGEnUcsMs7SO1xpUm10pGjUA1DM0ztZcdAJuEssrtIw3BlHOt5P/TNNs2J3Wjf/86jF/5\nQf/jdpgZ62iM0SlWHSpowZxqXbEZs8IWQb1xzZs0CKvvMAyxvb2Nvb29xjfLthCZNkGEUwIoLH9X\n9RBayfkRkwxBqky5L6mkTulIlc7tL55WJ6q6wrizQNRxAsw220UfZqxRJYjULGYWNsKmI1W+rn/i\nmLX8q7A+ti7SZCJrcViqVqI2VlNHPqo5J8Khz0XMVBt5mtRt/+V1OtVKV5xXkCc1NNAEoVpFp2Yl\nC9ATKhWyaiWrwgLzcJQ8A9YlFNAE2/dbB2MM2zOje9536DA/dMRqxZjnJFnU8giCYGFW36vAqole\nkiQYj8fFeK6SVK0CRQggkfKpBKkqrKi5f8iW7Pyng6n2kiAFTUIYdDk8pu19yJXNSMGWc2UaGxNZ\nMhkX6NoXIWgNFUATaZqXaiVDnAc5hFAl57aaXU1NLFTVqtYfjXOgDULFEiSrklflULJ0oX8qTKqV\nMLMQFuwfeS3Gt36oWd87LAS+xhgiP0vO1VrlSzkdxIvYDhuELhRwYeiI1YoxD9Igmyjs7u5iMBic\n6ca9aiKjYpW1vuRx3drawuOPP77yN7fLDNUc/NaPZRN8zus26rLDXSAl3KugMSBevusmnr6EQCZc\nuhwf2zUSjYGhh9pjq1El+uCrqFGlMO2yHd50fdUtE6TJFUootjdBqEzxtPr3rEgMNa4APdHS5bu5\nwgDlbcLjek6VC6a8qkLJ0jg32pAqZhaF0pZmOVc07UICF4R53NdNxhgy2RKqlkq2Fg3b9zs5Oems\n1jcNLZrjrRs6YrVkzDMUcFEmCptOrHS1vjZJoaog6AEByciGPAl1qVOMlpNi3didxW4dKMPPTCYK\nOuKpI1e6iXt4CmxbXPtM5CpNso+JeJm20znQCfVGtJfHW5crFU/9iKMJKqnSkSx1Waxr46la6gia\nSxEUZEqnNjUhUNMn/I1AgJxw+YYGyvlUHkQVyMZMfXsswgJTJbxRkKu7XoPxqz7st/85YdUvlM4j\nZFVL5DmLXC1KaWuMMU5OTrC31xKn0g7LQadYLQzn2z90DTAraUjTFMfHx4jjGPv7+9jd3Z3bjbht\nxGqZoJTi5OQEYRhif38fo9GoMq5tGJtl9WHw0duq7n+qGiDnpwikkZl0nZVM6RBN7CoKUBppABm5\n0hWQVSHa6GpUiePOuk6338hADFzfzbQPoRqJ7WUS5DNm80ISVY+lkjH1WnERdnm9rq08rtMn/PpY\nURblgsGOvLzpiXmdnFNl+63qiKh8H5f/T9PS0IIEGH34Vnv/OjTCsoijMMYYDofY2dnBaDTCzs4O\ner1eYYwxHo8xmUwQRRGSJAFj7Mz3fJditb+/f6b9dzhn4Hx9PxoQQl5CCPlzQsgDhJCfNrR5b77+\nK4SQG6TlDxFC/pgQcj8h5Euuoe0UqxWj6SSZMYbpdIo4jovwtHk/DNpAHmQsI/RNNf3YtDwqFUUI\nYL9fTu7EBFSXRySbVshwjaHOzMIX8hu3aJL97avauFQp0WbWUDbVuU4tXNtoX5rJd5OQxGhSJ7U+\noUeqwheN3UWFY00bFTqlS9suJ2SyiuWqHWYDTcqxV5UnlxOgWutKzZvSGVbY3ANVwxa1vpW8jBCD\nmUX3+F4HyMYYsqqlGmMA0LoQ+sL2TO+I1QZigxQrQkgPwB0Avg/AowD+gBByN+f8q1KbWwBcwzm/\nRAh5LoD3A3hevpoDeAHn/O99jtcpVkvGrKGAIuzv6OgIAHB4eOgs9HuWPraNWC2yP0L9S9MUBwcH\n2NnZsbpDtWFsFt4HMYkUzm1pam7bFGmUTciFiYX8/1khHhIm5UdAnpzqlCs19EpWW1QXO5vqY1Ne\nUpOaZei7zj3PBNf3N7WLxn7b+pwntY06FiqJSaPqsiZ1q9RtVTQlsU2hOzeh5rqQf6+xj0Ngfv+R\nyZeoIScIF6NLVa3WORSwDfd0GSI0cGtrCzs7O9jd3cXOzg4Gg0ERqi5UrTAMi5BC1/cwnb/T09OO\nWG0aVq0qLVexeg6ABznnD3HOEwB3AfhBpc1lAB/MhobfB+ACIeQp0nrvm19HrFoC2w1RF5523qvA\ntwGcc4zHY5ycnBTW9C4nxTYQq0VPbooQQHGcNC3t1oVawFk2qdWFS8lKQBpnH5rYwwSBkmDJn1kQ\nnvjXLvKZ5NoIlFinI0u2kEPTumhcDw9Tx0EoPkWYn7Lel1z5wLYvmRjPG66QPxto4i7+C5Rhf/Ek\nC7FTl0dTgEpvdcW1bsqd4ry+Tn0rLJ8rnUJlgkr4SZApVpx1IYFzRFuJo1C0RAjh7u4uRqMRhsMh\ngiAApRRhGGI8HmM6nSKKIqRpWon0sBHjjlhtIDhb308dFwE8LP39SL7Mtw0H8GlCyJcJIW90DW03\nO18xbDdyzjkmkwmOj4+xtbWFg4ODpRSkFeRh1QRCYBFkJo7jpah/5w2Dj96WvRXXvem3qVZyboog\nRfNQC85CsnzIFUszIqZdJ5FGm2pkI17haZ0o6YrjumAkYppj1/Y/1Y+FjjSJZT6EygeC4Oj6JEMl\nDjrCHhvy01yQa43NS8GS70fi2nDlVfnmtSVR9knjzDBEjE0SZv2XxyboZeTqgz/crP8dKjiPapys\nam1vb2M0GmE0GhXhhKL8yng8RhiGhTuh7lm6CFfAT37yk3j605+OS5cu4V3vepe2zVvf+lZcunQJ\nz3rWs3D//fdX1lFKccMNN+ClL33pXPvVIceqVaU5fj7/53+Df3H3nxcf3bf1HBXTTeD5nPMbANwM\n4C2EkO+27aQL0l4ydDdvQRzkdcKVrt/v4/DwcKkKVdseMPMkVowxjMdjUEorD6FV9GVWLKoPg3//\no2WYUX+rtHgGMlLV65WTPF1+h5g8+5pUNDWzEOTAt0gukDm6Afb6VEBGrnwc6QTUCXqT4r3FMQ15\nXqZ9+eSF+cBFjHRhgq59JNPqm0I198oGnbqkjretDhhQbSv6a7PN1x1bvt4nx5LVOQN6+bU6Hdtt\n2HV5VZyZybNo7xUeKOVhCddNKfdr9BuXMf7Ru937mRHnkXxsGoQxhmz3LrsQpmmKJEkQBAH+9E//\nFF/72tfwnOc8BycnJ7j66qvn1g9KKW6//XZ8+tOfxsWLF3HjjTfi8uXLuPbaa4s299xzDx588EE8\n8MADuO+++/DmN78Z9957b7H+Pe95D6677jqcnFhMYjrMjjXKsXrBt30DXvBt31D8/bMf/wu1yaMA\n5Av8amSKlK3NVfkycM6/nv/7N4SQ30IWWvgFU386xaoFkCfKIuxvMplgNBphb29vJWF/bSAQMubh\niBSGIY6OjtDr9XB4eNiYVK09SCAZVaTm5Hh5uRretwjnPxXxuGq57fOAiCdulzdX+JhvUdlaTpGj\n9lMT6IwfdPvXkSeTajXP0EFbH1z5UE3QVHmqEChp27PkDsr3pEgz3mK9D2kyQfyeTE6BgP1lRwcv\nrCtplE0xCCEYDodFCOHx8TF+67d+CzfddBN+5Vd+Be9+97vxC7/wC/jsZz97ZjLzpS99Cddccw2e\n9rSnYTAY4FWvehU+9rGPVdrcfffdeN3rXgcAeO5zn4snnngCjz32GADgkUcewT333IM3vOENrZqH\nrBVaoDQt7FPHlwFcIoQ8jRCyBeBWAOpbqLsBvBYACCHPA/AE5/wxQsguIWQ/Xz4C8P0A/sQ2tB2x\nWjJMipVw+zs+Pi5UqlVO/NtErM76wJOt6Q8ODs5kTd+GcVlEHwZ3va6ccMrkiNrC/zxNFRY1YYkn\ndVJhI1k+eTemNmJsolPzpN5GGlz7Ne2rll+lHKNpiKQPsfGqYaUjcx5tKu2VEE81HLBSu8tQ90rX\nVnssXQ6coX+m5abcqnha/S3I16AgVWKZ7nfbhHjpzCyEYyCjGP3GZf99ddg4CAfCXq+H7/u+78Nd\nd92Fv/iLv8ArXvEK/MAP/AD+9m//Fu94xztw5ZVX4pnPfCbe+MY3Igw9XTwlPProoxUF7KqrrsKj\njz7q3eYnf/In8Uu/9EtdLvkisWrys0RixTlPAdwO4FMA/gzARzjnXyWE3EYIuS1vcw+AvySEPAjg\nTgA/lm9+JYAvEEL+CMB9AD7OOf8/bUPbveJqCcbjMXq9Hg4ODpwGCsvCqgmEwKxEgnNeJPLu7Ox0\neVQGDD786sxWm5CMSIliwED5Fly+JsUkVYRH6UKjaFKaWOgm6gKuED0fiEm3z77iibtdPGkYFigR\nAl2xX9uxhQX4lmchYFuft3ar2/uSriQEBtvuZaZjngXq7zqNq/l6lXWR/bwAVfUtjc3hgKpqJXJX\n5RcJcu021cTCFg4og3P7iwUfxVIuFiy+j/x/pT+LCgnknK/tRLctz7pFwqTKBUGAKIrwspe9DM94\nxjMAZKkIX/nKV/CHf/iHGA6bl5zwfc6q4845x8c//nE8+clPxg033IDPf/7zjY/doYMOnPNPAPiE\nsuxO5e/bNdv9JYDrmxyrI1YrgCAKjDFMJhNQSrG9vW21+V422tIPYDZilSQJxuPx3HPU1lKxEmYV\nJChJlVorSIRM2SaU8qSUkHJibyMH8aQ68eRcP1n3DfeTyYBJUYsn7vwbG2kQZGhoyHeybdvU4U67\nf0MOVjxxT/iTsDkZEsTYRrZM6pSca6XLh3LlYtnIVJIAsqpvGluhQKntdYim+jGMDcsj6fpVCZdJ\niRJkS61lpUMSVsmnTMR0pIxRgDOMfu1mjN/0ifr6Dka06Zm3bKjmFVtbW7jxxhtx4403zrS/ixcv\n4uGHS4O1hx9+GFdddZW1zSOPPIKLFy/iox/9KO6++27cc889CMMQx8fHeO1rX4sPfehDM/WlgwFr\nlGPVNqzn66eWQ873EfHPTYv9LRptIBCzgDGG09NTjMdj7O7uzj1H7byOiwmDf/easjYO4J+70pPG\nNI7qBVMFZsm5EiF+psm6PP41O2vDNirJUsPOTP04K2omF4Z9xhM9MThrH3RqobxPmTT5bKtur/ZP\nbDOPsdMdQ4xR6JmrZTrParifnGtVcYNM9MtdYbC6vDVbiKAOuvE35VqpZha9Hnbff5O9jx02Ci67\n9Xm6Aj772c/GAw88gIceeghxHOMjH/kILl+uhqlevny5IEv33nsvLly4gCuvvBLvfOc78fDDD+Nr\nX/sa7rrrLrzoRS/qSNUisOpwvSWGAi4bnWK1ZHDOcXJyAs459vf30e/3MR6PWzdZbxOB8OmLKJo4\nmUwwHA5xeHjYKqI6T8zr3Aw+9MryDXsvyCZlvX6mVqVx9v80rqtXQBkOuOgxFpNqV1iabhtX2Jis\nLNnULd33B7J8K1X5EhP5WcLkmoSYCfXHh7jqlCZT/9TJvOtvsS/rNooqpapQFVVLnDsPRz+gqkJF\nYRnSJxBNzedPVWZ1BhSAWXkqyBE3q1bqenk7a4igNIaE1CcLskOg/H/RB8D/WvLEuho8AOv93QB3\nqON4PMbe3hwcR3P0+33ccccdePGLXwxKKV7/+tfj2muvxZ13ZpFXt912G2655Rbcc889uOaaazAa\njfCBD3xAu691Pi8rRadYLQzE8YNrx8x6zTCdToskUgCYTCYghGBnx9OeeAk4PT3FYDCYKb563uCc\n4/HHH8cVV1yhvclSSgtyOhqNFlrrazqdgnOO3d055AbNCMYYjo6OcMUVV8y8j8EHfhgYDMvJlyg4\nCpSTuJ5SFJjRbMKbxtJ20vnoaZa5Jv5qGKAJ4iGwtWtWrNQHBaN24iRyeXQErKJaxNXQO1nFoHE1\nJFBVSGohlVH5PVQ1K5lW9yVPrtX8KbFeJkfyvtV9CGKlkp5ZFEWfB7KujbysP6wSMhuxiqbAQCWw\nksIkEyugSq4EWZLPgzzupuVAeY3HCjkTy+VzLV/HleWKq58c/qf7nZhUQvW3wTkqhhiqDTul4IwB\nhGBy2yf1+2yI6XSKwWCwlFqKy0aSJEVI/jqCc24lTzfffDO+8IUvdCRmNpy7QSOEcPre7111NxaG\n3ls/A875ys5LFwq4AvT7/coNrE3qkECb+mS62QtzimUXUF415nJuCCnJg68LIFAlVTJchiumUEEf\nVEKoLCGCMsR3M4YGSt9TJSy+bocCs9iwm/pl2tcsoXXyJD0J7SYiJvi4//nsVyVaroLBAjoVSQ3j\nSxKzY58LRfHgqf7at6lVFSdAbm/PeX2d+htuassufrdpXHcL7PVAggDgfG4hgW15HiyZY6EsAAAg\nAElEQVQCm6BY2Z6jHTYQnK3vZ8XoiFUL0CYSI6NNfVLHKEkSHB0dIU1THBwcYHt7eykPxraeqyYY\nfOiVmSIgigADmTpFUyk0UFKv0lifq2Iab5FzFUfZxFhMjm25WL4oJrCeBEu0PWsbEXrXpH4SjedX\nt8kErQ2557j4hPXNsu9oWj/PPue9kkulXG+JR05csW1a9kMH18uDs8JkvW5bJocV6iD/1pIoG58k\nLA0skjBbRtPaWHHOsXPHixp8ATPWmXxsOrpzu2FYdR7UGudYdcRqBVBvYG2crLftJis7KY7HY5ye\nnhbmFMu0p2/TuZqlH4Pf+CEpXCgtQ/tck01bvkYal6TJZwJcIV7h7GoD4+bJc6UdtRMxWd1S1SrV\nSt2E6NRslGDazqRORaezkR5XW9dY2Yw1XGiqhvmcc5vBiMt8RC38KytTNsi/g6lUJFUm1NPj8v/y\n9RJalMt4qn/gc+5fJDqJ6m3FfbqiWAVFKCBnFCToAUGA4a/8I7/jbCA2WbHqsKFYtarUKVYdFok2\nTdYF2tYnYU5xdHQEADg8PMTW1tZGPixm/c6U0mzSJbsAyhNUmTyZVCoxwRRvyNUwpFkRhbMrWtHU\n3yUunpjrJAFuO3QbybCtM+1XkCs1FE4lQbr8Kvm4s9q42xQv2/exuQkW+8n7JCuWlX2ojomuIr+x\nvnhvPPVzeZRRIVDH5nazQiZcOjJne/jXQgTD7KNC97tTX9oFPXBGAcZAemf7nXaT8/ML27M8TdON\nCKHvoGDVqlKnWHWYJ86LYtWWPlFKwTlHFEXY29vDaDRaWaHKNo2LL0Qu2vYHfghgrK7KCNWq2CCf\n9KnGCz6TaR2aEi85fLDpdoCHFbZl32nqJmmCcFDNZN4npwuYrZCvbf+1dlH1e4r/+46rehyd4qfL\ntZoljwvQK1g6EiXDRqZ0ZKYJgYrEOVYKBkeakFBG9fbqAlZLdReR9xhPg2pF1Hsk49j+1Re497eB\n2ATSaPp+Jycnc3UE7HBOwNj6flaMjli1AG2crLehT7I5RRAE2N3dxcBV4HND4Ht+0jTF8fExDv7t\nrZkiFQQZYZInhmKCKgrfqqBJfcI8ZytnLaJpdXLtcz36EgdXu3BcJ06VSbZDIVHXJ4n5mCYiaGqv\nIy9NiaiqeM2r7hRT1RZNrpVMolyqlYt4yOSqqWoFlASs4vR4hhwstdaVzbBCfDfTde1FqrJHOJdC\ncLkUBslpWoQCkl4PYLwLCdxA2IhjR6w2E5zztf2sGh2xagHaQGJUrLpPghAkSYKDg4Ol5lHZsOpx\n8QXnHJPJBCcnJ3jSXa/KiJCY9OnIkzCrkAmTqkC4yNSi3vjq8rDUCXyl/dRPvYqm9vXqpF+GbfI9\nC0lpkmfWJIZcR7hmUQMBvzDNWRQr2zjLiCZ18qQ7fwVZchAk03pfJ0DxOzKpVTIxUs9ZEtnPY+R/\nDfH8vPAkLkgVT2Lw/PvxNOsnpzQjV5xh61/91977L46zxqrOOn83F05PT7G/v7/qbnRYNlYdrrfI\nz4rREasV4DyEAq4Kot7GyckJtre3sb+/3xpS1SbYrhnhmEgpxeHhYfZWm1GgP5BcAAd6giXgazku\nT3RFcn3tM2N4mApTiKBpgupDIGxtGLUTHnmdOkk3hbFFU3c+lEw0dO3VMD+hVpi+i8846JQlF5Hy\nCdnUkRTX9RBH7jBAAZVoGQ1ENMqUCjW8r1juoWCpSpUNOtIk/5Z9bdfz3CstIZDDAgmphMeQoAfS\n62Hr3d/ld5wO5x4uxaojVh06zA8dsWoB2kisVtEnYU7BOcfh4SGGw2HxMGjLGLWlHzoIUio7Jg5/\n7Zay2CpNS2XKNMFUTSt0KhVNqw5lttwa8TAXbcTHWO9HIkmmcW6iuJyVXAF6clVYes9AGtVtBJEy\n7avJMXRW5/MIHRSwkS2xz1rulSuPyNEX1Q1vlpA/03F9w/5MfXSpVXK8v4/1unwc0wsDk5mFgFwj\nUcqzIr0eOKXgLC8ezDkG73qOeT8bhHVXrGzPrNPTUxwcHCyxNx1agVU7962xK2BnBdMitOnmvkwC\nISzUKaUYjUbaPKq2EJq29iNJEozHY/T7fRweHiIIAgz+l5eUIYDiupLJlTCn4Mxc+FdAdv/TtZvF\nGVCeRG7t2NuaJqDqdjq1IJoCw7wdteQzqWYdMmwTcNO6cAJs7/qHugHN2srfqwlMJDiOgK2hfpmL\nUPn2o2kRXAFbyF8aly8P4mn5f0B/bmhiPtdy/xgtr3X5dyMvZyzLW6wtp/rfidi/bn00cYfTGgiV\n9r5EgvJ3Q0jtRQVpEAnQhnteh7PBNLfoQgE3E91venHoFKsVQBcKCLTrQl8GgeCcIwxDHB0dodfr\n4fDwsDOnaAjGGE5PTzEejwuVqnBMDHrZp0lRW6A6ibVZqs/zJUA89Z90+4ZNyd9jVoXGZ3u1ZpJc\ny8sYEmggN0YjC5Oa5fm9bKqVK+RPa0DhsIdXVUlVtVL7I6tQOvt035A/3Trd9W+6bpq0NalG6nKX\nS5XVel1a52NmITZLE+n/kplFXteKBEGuWrFGqlVbXvzNG216qbkI2L7f8fFxR6w2EavOg+pyrDos\nGm1RQgQW3Z80TXFycoI4jrG/v4/d3V3rg60t49OmfojQSUJIUddLYPC+m/IiwEn2Br/iaJfmH4ML\nIGCuYzUP2MavCcEC8jwoz3wcdfKvkhhVrXBtL0Atjn/W/oR6hUruh3oOfAwkZlWFxP5nqSXmA11I\n4Fn6KqNpMWGdC2CT4sEyfO1947B67etqXRl+GzyaOu87PE0y04qc2LMkAhPGFWkKlhMsliYZqcpV\nMxIQ9N/5D/2+Q4e1w3g87kIBNxGrJj8dseqwaLTtbdmiCITsVre1tYX9/X2v4oRtITRtAGMMlNJK\nXS/5+hm876a8CLAm/E9AdQFk1C+/yuUMKCsRTa/pytv5hgQrmvgRLNc+Vee32nGmdYVKXjfLMWXY\nCII210u1dY+qx5TPxzxzrWoK1AyET6da2ezTVVXLtn/R1lZfygSZdE1P9G1Mtc7k5fJ1ZKuNFk+t\nqhX3OEcsqV83pAjdlX6HRFPfCpmhhY1cbbKisw7o7NY7qOCcre1n1eiI1Qqgu8G1lTjMs0/CrY4x\nhsPDQ2xvbzd6mLVhfFZ5nkSRZKFS6ep69X/1ReCUlpM6OYTPJ1G/Sf6U7PwnE6GzFIoVEGMcT/0n\nx5z5hQbqyJM8NmdR6tQJrqqG1BSoOZCxJm19zou6P1+S6wr384Etl0pFk/PkImXLhHz/cPSFK+qh\neu9hSVwlVQ7Vv/h/EBT5l5xxcM5Agh56P/dMjy/Q4byhM6/oUAPj6/tZMTpitSK03XJ9nm/vrHlA\nK+jPPLDsc0UpxcnJCcIwLCzoTWNCer1MkVItowvTCkm9SpPsY4NQEtK4JE0+k1oxIZc/s2LeRMPV\nf5nMqeGStv3b1rmswH3an3UcdEpT0/NSEGiLSuWzz3hqz7XS/W1D0219lCmgHkZbOP7JFuvMsFxT\nJLiybw2RzO8t3OEGqVOpVJhUq0qbgIAEvYxc9foI/vl1zv2uE9r03F0kbOYVHbHaPKy6iG9XILjD\nwtE2YgWcvU+qwqLmAS2zL/PCsgmeMPg4Pj7GYDDAwcEB+v2+djz67/me8g9bMeCiTS6Z60iuaqkO\nzMesQkymZ1Ez4ql/PlV4al9PU/e+bEqZrS6SaSLtWxvM1d4UBjcPJUbsY16qTlPrdRfSWB/y5woN\nFJgcm/ddIVBJoyK9XpDPJ+f1MEwphKUgVYZ7Hosjcy6B4XfKkjjPw4rA4ryYsKJQc8ZAer0auVr3\nUDmgfS/v5gnb+etcATcUq7ZEX2O79Y5YtQRtIQ4yztInVWFR84CW2Zd5Y1l9EWMYxzEODg6ws7Nj\nHMP+e74nS0Tv9SouYFrYVCofBcuEpud3VjIgW1b7tLMhmtRDJGWy5EOumsBkTGFywqs46znUHV3I\npo9qZWqnLtedL5V8q3+79u9C0+1mMbHwOYYc0qkrJKyGl9rCTqHkTSmqFY/sOVesgbkIiyPwJAGL\nY6W+Ve5EmyTglIHTtCgcjKAH0u+DvOPprbnndlgcTk5OOsVqE7Fqg4lFflaMjlitCG0PBQRm6xPn\nHNPptKawdPCHPIbC4KOn1JyRz03vXz+/cPniaQoyGJTkqjfIJoJioqY7n4JM6dzNXGYV84CaR+Vz\nzamTfNNE1IeENQk3a1JQVm07T5dFH4XmrIV6ZyVD6rnQ9aNCxsLq8ZpardvGVXe+fF4cRJPmZQp8\nIF2H3vdWqR1Xw/8sipZMwCrPG5mAS8s5TbN7AGfglIEEAcbjMSaTCZIkAecczNcB8RxhE9Q4l2LV\nEavNw6rD9ZYdCkgIeQkh5M8JIQ8QQn7a0Oa9+fqvEEJuUNb1CCH3E0J+xzW2HbFqCdpIrIAGD39k\n5hTHx8dI09SpsDRFm8ZnkX1J07Qyhl4GH4Rkyej5hImnKYggs/LkUJ6AigmeblLqPN6Cbhs6RcQl\n6/vm8thgy4NxhQxa1xnULp06JZab2vvCNyTOpCy54BPC6bNfF/kywef7qUpf0c7jGDbiLO9T/l3J\n4YUycZrqw1G1Ln+5asXkumfKGLE4hMvxikUhmC03S6NaZfeP+gsU0uvh4JeeU4Rvc545uo7HY4Rh\niDiOQSltzX25gx6u85OmaVc/chOxalVpkR8FhJAegDsAvATAdQBeTQi5VmlzC4BrOOeXALwJwPuV\n3fwTAH8GwHnD64hVS9Am4iDgS4oYYxiPxzg9PcX29jb29vZqCss8+tK28ZknxKTl5OTEeww55yC/\n+DxwRjPFCqi+gXaGBMb+ilQaV10ATZ95wJSDZTr/6iRaW4PqjFbsupBBdd9NFKkm+VOAfjzmbeih\nO4aL8Pjky+lMKlzXiimXyvS3DTayFE0cipem3pUHauRJFyaoQBAi3X2OhZbzl7e3EiroVSuufqec\nZJFekLsFcgx+5hno9/vo9XoYjUbY2dlBr9cDYwxRFGE8HmM6nSKKIqRpeu7u05ugWAH25/kmfP8O\nG43nAHiQc/4Q5zwBcBeAH1TaXAbwQQDgnN8H4AIh5CkAQAi5CsAtAH4dgPPH0sVorQi6UMC2hVm4\nyAznHEmSYDweY2trC4eHh43d/s4j5k3yxBj2+33vMSSEYPS+7wV6QT4R6oMzCtLrg/T7VdVKkCfO\ny0mkSqjkv0UbEpSTSQ/VLPsymgnzYFhfJo+f6S18EmaT0K2d+jpdcV9dOxnRJCuWbIMt/CuNq9vL\nE/JoUq8VBmSq1XBkP6a6L93f6vcz1a8SbQH3OdONWRICg+3y/zrIbUxIIv15N/YldLd35U/Zzm0t\nLDMB+oa39JNj/bnUwVafSgOVcFUm9YzVjWQ4qynEnLPS7S+Hi1RV2irhhFwUEea8qHHFKQPp5f9n\nDIOfeQaS/+GPQAgBIQRBEBQqB+cclFJQSpEkCcIwBCEEvV4PvV4PQRAgCIJu8r4i2IjjeSPBHeaI\nFpg8LBEXATws/f0IgOd6tLkI4DEAvwzgnwLwipntiFVL0EZFxtYnSikmkwkYY9jb21t4KEGbxmde\nfREqVRzHGI1GMzkmihAeQarUN9A8SUCGFhIlICbRLgVrljBAMennHNhyTMh18CFNoh1gn2C7JuC2\nY9Ek+/gQJRnROMt1U/sB6I8VT/2VRFN/1YlUEvmNoQ5eRCpv0yQ0UyVfrr9VpLG97pV8nnVqk6xi\n+lwXYj89XZhtSdT49LQ4f5zSzBACAJuOy+K8jFbOsWpIIU+GC9LEeNU23bCtDiy2kFJCihcdIlez\ngiAAGMPOz30H8M4HNZsT9Pv9IpdW5GKJQuZxHINzXpAsQbjaQrQ2RbGyYdO//yaCt6De0xLh+2XV\nHwIhhPxjAP+Fc34/IeQFPjvpiFVL0CbiIKDrk7BQn06n2N7eblzkd559Oc+I4xiTyQSDwWAmpW90\nx4vAkROrfPx1pApAOalUJ+tMLiRsOYfzPL8iz8VHzZAnePE0J2YacqC+eVMnyeqkWiYjpon5LCRE\n3s43VK3JsUxt42md8OraystkW3WbaqUu1/3ftExXMNhF0AR0oZvxdHbSrFsnkyT1uCYCJYFHYUmU\nzgAaTWsKVLkuG0PTPZZGofP+60uq5HssCUjmFshooaQRAOxt/wDkF79mPZ6sVtlULaFkyUSrm+DP\nHy7FqhvzDcUazad+768m+L2/sob7Pwrgaunvq5EpUrY2V+XLXg7gcp6DtQ3ggBDyIc75a00H64jV\ninAeXQHTNMV4PAYhBAcHB3PPo2rSl1XiLH1hjGEymSBNU4xGo5mUPvKLzwPJQwCFC2CxLlethJJV\nCwcUkPOrdA/WeRtUqOMlT7pNIVm67ZuoV7Z2rkl6PK2rTAI6BUpMvm3kx9Qfk5FF0/2cBTVS5Pjb\nFz4OgfK10VS1UiGPpUuFsm0rgUdh+TsCKqSLM1aSqzQpX25IihSntAy3k9vrIIUDClJVXZ+pVpwz\nO2GCmVAREtRNMCSChaBXvHAgQS971ctYrooH4B7kqn5Mf1VLVraWMelfd3Jhe1aNx2Ps7CzgftKh\n9XAZ4ZwnfPdTt/HdTy1f2v1P/+nv1CZfBnCJEPI0AF8HcCuAVytt7gZwO4C7CCHPA/AE5/yvAbw9\n/4AQ8j0A/jsbqQI684rWoE3EQYVqrKCz/15mX84jhNInF0ueKXzynd+Z2apTVlqrS4pMLRldBaPz\nsf2WJ8hnmZRw1tz0wlX8V64hZFoH1MdBVSZsYW22dabx9XX9U4veuupXJZG/G6D3Mg8i5dNmJudB\nyzau2l824xJ1W8DbkEI1guENcpqMYBQsFoYVmkmOtZZV+V20ZhcO0lWB7BQowg/TtHQNrHSJgXOO\n9Ke+xX//2kOSQtHa3t7GaDTC7u4uBoMBOOeI47iweg/DEEmSgOXH7tAcXXHgDjWs2rlvia6AnPMU\nGWn6FDJnv49wzr9KCLmNEHJb3uYeAH9JCHkQwJ0Afsw0cq6h7RSrlqCNxIoQgjRNcXR01MhYYVF9\naQuanivhmsgYw/7+/sx1vfjPPgvB1lZWwNMQ/gegrlYBRf0bke+hzeGRl1WIU37Oa3k7UpuzqihC\nufDNwWqiXJmUpyb7aQIlf6aCeZDaOLSPkyskb5b6VGIfNvXIJ8zTx6RCd2zft6s2gxEHdMqU01kT\nVRVKzqkS14EgT6qlOY2iwiCiAsbqBhNyztWMSpUMoVrxNAE4L/MtpHFmIpSY80ytKvpPEQBIf+pb\n0H/3XzmP5QsRGqiqWiKEcFGq1iYoVjZitbe3t+QedWgFWjbfXDQ4558A8All2Z3K37c79vG7AH7X\ndayOWK0IbQ8FZIwVdUr29/dbUedCjNGqH4K+50rORxsOh9jb2ztb3wnJJnEAIFwAg34Z/qfkixTF\nRG1GCGkCDLaAJK46kol++oYEqpP1WcmKmJz7EKx4mk1eh7vmNjTNPjZnQRu5Eut0eTam7dIEQFJ+\nB5n8mkiXNX/K85ox5VWp51AXXucia8ZjWrYzWser4X5K7pVPLpX6t2/In6NtxU3TsE6YSai/Nx8T\nCUAlYpL7Xu72x+KoPOeKK2BBuJRrQtwXfZUqppBtEpCMXJGgJFdyeCCQ5VtxDvC8BhbjSH7yqRj8\n8n/2OmZTyLlaRb+V8EHGWEGwZKK16mfEecHJyUlXHHhD0ab55rqhI1YtQVuIlUwG+v1+xVa3gz8o\npRiPx+Ccn0mlEuA/dz1Ir1dOyBgtbNUr7XQugDmINEEpFCxCMlJVaTiHSYk8qZ6FZIXjcsLu+l1E\nEzu5Ev1x5lQpeTSmdbbtfDCP/CkToWlCxARMoXe6YwhSZAsDbJInNYt6BtjdAGXyFE3rOXzqMS3K\nlO6FRRPQ6USrSmnzpyoH5rXzyOLQ+qLDh1SphApAQaAKcgXleZTXtuLKmAcBAQMWSq5U2FStNE0R\n52Mgm2K4rN7b8LJukXApVl0o4IZijXKs2oYux6plWCW5opTi5OQEURRhf38fw2HDkJ0Foy3k09YP\nzjmm0ymOj48xGAxwcHBwZlLF/sV3ZEWAadXBT367Tnr9jFT1c8t1zU2TJ3H2oZpJ6SJDPKNJNplV\nJ7SuG3sc+uXxiGO44JrE245lW2c6dhw2KioLwJA/JR07TerrXdB9b9124jiuMa+FFmrOk23/uvW2\nPLIk1IxLg4LB6pg5IEiWqzaUHIZLpxNpub4AcIWYSP/nVAq/06le2vyr6v2HxZEzGV1LqnQgGuUa\npQMp6QWASGXICVn01qv89j1nCFVra2sLOzs72N3dxc7ODvr9fvGSUORqRVFU5GptEmzPzOPj445Y\nbSpWnQe1xByrZaNTrFYEXSjgqkLdBBmIogg7OzsYDocghBQx7W1BW4iVCYtwTaTveDpIfwAS9BDk\nRhVEeQPP0zRzC9MgCzvqgadJc2towwTrTBCTfFWZsZ1Xlz26QDRx5++YVCEfAiQUnCZkSbX0lo0p\ntnbqhMBHfZP7o61XtV39uwlUgqQ7xizQ9UNLvmZUsFRYiBZPYpBBVb20KVPyOjo+NYYKqjCpUibC\nxoS1uvidSqoVL2rB1QsGs8h+jrwIVa5aie/K0jK/SvzLGQPp9cBSiqDfQwAGhiC/xxBM3vLN2P2f\nv+4+1gIhFzAWMKlaQs1ijK3MjGlZ6BSrDio2rI7VUtEpVi3CKohDkiQ4OjoCpRSHh4eVulTrHB5x\nFqjnSXZNHA6Hc3VNFKQKQEGq5DfiPE1rSfEqTKRKd365qgQsCjoFS8AU5qW2tznAuY5tXKdRmeS/\nTaTKdFybktKERMShv/KiU5zkorwCSTSba59WAVMJmU+hYIeluy6XCsjC+4CKaqV16ZOVI2F3HtX7\npSM6dOxwnhTHpWmxfeV3SfWKlEm1soFFUWUf5c54re+qauWtUqE0q+BpUtbVqihWQfG9aELBWEa2\nWD5BC4IAk7d8s/fxlgWTqtXr9SDqa4m6glEUIU3TtVK1XKGAXY7VhoKz9f2sGB2xahmWRawYYzg9\nPcV4PMbu7i729/drjn9tU4ja1h8gU6mOj4+1xPSsYP/8GVldG6CwPq64jikQb9I5o2BpUr51lmEg\nYSJMEAB4HHl/iu1Nifuu82UjWNmXqbd3QS7yaoJtUms7hm2f0URPfnzInk97W16RD2ZVg3yIlA9m\ncURscJyiILbx+OV63QsEV6mCgkB5OAVShypVaz+RQgldk/r8N1EhVZrfmS+pYnFczc8qXqyZQgJJ\nTSALAoKglylF4zd/k9dxVwWhaA0GAwyHQ/T7fWxtbWFrawuEECRJgslkgvF4jDAMCxOntj175oHO\nFbBDh/mjCwVcEXST72UQB1EjZDKZYGtrC4eHh0Yi0DYi05b+EEJAKS3ecO7u7hYP5Xkhffu3IRgM\nMoUqd/8TIUDirbGOYLEkKZLlbUoWT2JwMYFyhQjaEr8VckW2ZszLa2Tc4NE2mtjNKlwhdz5OgYA/\nWYgmepML03Giib6os6/phVCDXNek6sgniMyggUOg2Ka2L8m0wmOSL1Qn+RqqXVOe4y1IRyCFzbI4\nMr6UcPbNQLpYFFZCCOUXH3IIYcX9Ty4SbLPmB0DDaUFw5H2UB6ybXAAoLN5N579xnav8vkuCoCB+\nhAAIgiwkkPGC25GAYPzmb8Lo/f+f/zFWCM55xRBDLBNqlgghlB0Ixec8RHW4FKvDw8Ml96hDG9CG\nudS6olOsVohlW64Lc4owDLG/v4/RaGR9MLSFyMhoQ3+EFT1jDIeHh0VO2ryQvv3bKuoTIUERCiTe\nlovJWxEmyHlZd0aBrGAVypSrv7426+qx4gg8Ct0FVGUlSpxTl3olKzau4r9qG1vYoEmp0B1D2K77\nFvu1QWdU4YK8f1e9qrnkRglDiwaqVZPiyQ1DT2the0lcudacqpUEnsRIT0+Mx7ApU/I6lXQ1Vau0\noYSMGfcDZISr3qnsd8R8DV9s0KhWLM36xygvwv8AgDGOIFexSJCpQSQgOH7TlWfvx4ogq1rb29vY\n3d3FaDSqqFrj8bhQtZIkaa2qZetTl2O1wVi1wURnXtFhGVjU2y/OOcIwRBiG2N7e9g5XaxuxWvXb\nQcYYptMp4jhGv99fWAgF6fez75rnNJB+UFirV4r+pgnQy8+PKAqsvNGWFaxlQ6dAOLehFKBTkKFD\nkcrbwdXOZbPuUrZs4WEm9cRkTNHUZr2piqeS4UgZH0G81H2qSpNpmTiO2s76t8XK3QFdPpQPZHLF\n0qSiWjm3tShTQLV2lcs1UOyvVK0kNUtWrVz7yOtbZftg9RDfislFbFwHNFSqNO0FuQIyQiUmMZTy\nTNhiPK9xlYUHHr/pShz82l83Ouay4WsYRQipqVpqXS1RwFhWtlb93ALMz86Tk5OOWG0qWjS3Wzd0\nxKpFWASREU51QRDM7FTXljofqyR6cRxjPB5ja2sLu7u7hbPUvJH+99eA9HpZmB7nxaSw8oY81dup\ny+CU1RLeiUaFauwU6ILm/IhwwUYEK59UO7dRyYOArFCpRWHVybNv2J/uGHIYl1r7qnEh4IbFmM/6\nm3TlL81iSOEDh2qlhv+pf6tkiadJxSmTRSGIUntP2JjL5Ea49rEkQWCo1WcrGFxpJ7sKasL7TCRM\nqFKlQU3Wv6K95fepuy8XxEYD7+LBhnxJ+f4r/z8ISCUUMFsWAMjuP+eBXM0CuYCxqPUohw8mSYIw\nDCvtRB2uZT5PO/OKDjq4yjN0mB0dsVohVKIwT+IgnOriOJ45B6gNZErGKogVYwyTyQRpmmJvbw+D\nwWDhpCqPqamtL1QrkUMl3oTnluqA9LbeoGABAEtT40Sy1jaJEOgK0TYFZyVZcqlMxTYcPApBho7j\nC2VjYFOmHOqWIDxUE0pmIkOCEPh+n1nQQLXikUbp031v3T5nMaNAnfTowOIIgaONathgNEPR7NvZ\npkEdK5cyVVWg6hbtTcLwbKF+KoRqxZLISMCNxMkSJlzdXlc8GIByy5VSrqr5V2n1IQIAACAASURB\nVARAXmSYMVaxcz56w5Nx+Ov/xdmHVWCeLw6FqqUWMNapWrKytapnbadYbTA6xWph6IhVizAv4iDM\nKQaDAQ4PD2tuf7P0qW0ka9GQTT6Gw2HF5GMRBC/+p9+C3nA7C4UjQRb+R0gxeXM5ljWtUyUmWpXz\nanzTnU828wmdWgOoKViY5TYFLsKUw4dcccYAUzuRuxJNAVtYWDzVG0y41pn6pCM6Yl+KolGoekON\nKYahvfxda0REnuCbyJXjN60jTS4iVZhG+LSRriNVddL1Rf7NuVQrG3QFfK2q1SwESlKt6HRcU6Sy\nNqxQpDKDmrx9OC1/l1IbpqllJe7NWS0rsa+qasVid04l9ySfOtWKUo5ejxR5V8LkgYEBef4VQ4DH\nf+S/whUf+Buv46wLdKqWSrTEeKnhg/N65tqe32EYYjQazeU4Hc4ZOmK1MHTEqkU464SdMYbxeAxK\nKUajUXEjX2Wf5oll9UU4/jHGsL+/X4mrX0Q/krf9g6yIb0Gq+tnETPNmnPQCsDwssNfr5zlUSsiZ\nGoYUx5mbV/EFNATMQKp0UPM4ZiVaLAqzcEcPgsWmY692ThKWJlVy5VlLyAoNYSus6wW5UpQwLyXO\nAd0+jGTOx5XPQaRMKtK8VKtK+yRy5kbplKjCCCJJinBAHZFjGmMKkzJlg9wunZwi8CwebCwSbDHz\n0LoCQlKaNMWDaRRmL0QM7oFiexIEFce/CnLViqa0MheT74E0zc11lNuifFgSkFaSq2W/OBQkSlW1\nRAjhPFUtn+fUWV68dji/cJZ16DAzul/UCjEvV0BhTnF0dIRer4fDw8O5kKqz9GkRWHRfxDgeHx+j\n3+/j4OCgRqoWAkIytUlMihg1TurEhJAEPT2pQvb2madJVrzUErbY5EGty88CshAlFofFZxboXNFM\n7VgUVgu/6tpNx8Z1nKZWU4SKm6GiEtqcDq1GC7rwQtt+NKYYTYwctEVwFVLE4sjLfEG7f5GvZAnD\nE8fzCtUT+1OIkkqcakYKanHcBiF/OgVYFy4nrmm5fTrxKx4MRsvvxvTFgyFNbiptlPtczVFQyo/Q\n3RPlMDxj9+LI6/wAGalSUbl/SP8PgiALBazkXBEEvaAgVx1KyAWMt7e3MRqNsLu7i8FgUEROjMfj\norxHkiT5+Po/C7XF4DlvzbO9wwrA1/izYnSKVYswC3EQ5hSEkJnNKebdp/MISinG42xC7hrHeY5J\n/FNXF6E+JJ94AOVEThAsMck01eHhlFrrW5WdX+y7lCJciUlKlEeSrFCvCvXLMr4+6geLQqvCpVN2\nhEGITU0q1ukKzBrUIpMBguk4tiLQun0AOLORhUyWfML/VFKlI1k6MiefV5bEFRXJBmqwKrehifX6\nWcBpWrzwYGnqVK1YHGprzPEk1hqesLA0NlFVqxoxklQrkcNVuApK8pG6nXApVFUrmrLKOavkV2mW\nqf8vc64yB8Ggl4UI/t3rnoRv/ODfGkZoeWjrs81H1RLtZGWrZmbiocZtWph/hwxtvfbXAZ1i1SI0\nmbALc4qTkxNsb29jf39/7qRKPlYbsAiSxznHdDrF8fExtra2FjqOKgSpIkEvy6PK31gXqlSvfKhm\nf1drVwnI4UO6Cbkz96pBGGATFAqTBNf5q9lFo/omv9i3jxLiUrcsYYB2daq50sOkukPyhJ9HYZ2k\nKMqLHFYIaEiMOplKE21ImW7MdKoVjyMv4lTbbobfptrPrO/lsZyqlbS9zgxCvnZE24JwSCqUGAdZ\ntbIpU7pQQhU0ipTaVPr/y6oVLKpVrQ+6WlZinSX00+e3Q1NWhPfZICbljLLiOqSUVcLLstpWpMK6\ngoDg7173JOf+l4W2kwudqrWzs4N+vw/OOaIoOrOq1WGzsOpSU4v8rBodsVohZg0FjOMYR0dHCytQ\na+vjKjFvYpWmKY6Pj5EkCQ4ODpZa32v61m/O3gznkyrOKIJ+v/LGm9PUalrBGbXmZNggJt8sicHi\n+meeoFGkVxwMY6gjVzqUYVbmCaBtEmmbmAJKzo3HRBrIyI/a/yYharpjq/uvLXOMl8sVzyck0Oea\nqJEezTY1Fcvn2JZcKlfbWnjhjL8XIPs96sibSqBspMsULms6h5X8qaIfrBYaWDH20BxDWCubihRn\nh8ja1AhV7TmFSrvyXwpKy/9zxsEZL/fHeVlMOH+Z83evexIee/UVxj4tGufZmEkUMB4Oh0UBYzEX\nSNMU0+kU0+m0CCdUCxgnSTL3UPdPfvKTePrTn45Lly7hXe96l7bNW9/6Vly6dAnPetazcP/99wMA\nHn74YbzwhS/EM57xDHz7t3873vve9861Xx3qEKGg6/hZNbpQwBbBNWGXrb+Fhfqq+7RszKMvQqWK\nomhmK/qzIPqJiwh6WV4V6Q/K8BxpQlYQLF3IkJgsihBCXb2komBoktXEAqr1bRwhgbpJcW+4DRqF\n6OXha8Y6GIb8DhpFCEzXrHJeC8MBNVROIVEsjipucCZ1yxQ6yMIpgm1N+J7DhdG6zzjUWtQbj5XE\nZ3Za1PZDE2qnVa3iGL2hv7GE2AaA+XxK7VxtnMeKqud43sTfemxLaJ9tnSl0UQ7lk50Aq26B9TpY\n5g6WroHA2YgjAKSx4brP1SaaMvT6QaZQISNVsnNscX9W1Cmm3BM458XyXi/AY6++Ak/53x8/U983\nHbIDIZCNcZIkSJIEQtWaTqd49atfjeuvvx7PfOYz52q1TinF7bffjk9/+tO4ePEibrzxRly+fBnX\nXntt0eaee+7Bgw8+iAceeAD33Xcf3vzmN+Pee+/FYDDAL//yL+P666/H6ekpvvM7vxM33XRTZdsO\nHc4LOsVqhfBVrMRN8ejoCEEQ4PDwcCmkytanVWAe5CdJEhwdHYFSOrPad5Yxmdx+JUDK8DwxgRf/\nqqoVgGpBYIs6IxQslsQZoUqSsxeRlSDe1tMo9K7BU0/Cr4cH1raR3/77KBoebWzqHwunRkWKRaF5\nXVF01k/NAtAo74dFoVbJ0IbvmRSPGSbaJoXRRmiKYruWNkW4nS73qthP2Jg4sSSuXI9CtSqMJyTV\nqqb00BRUCfljSeKlTNlQKejtMlsxqKosCqtqrFCdkkj7UqPyW9Pcn4pzqrl10YR6hf4BGkUL1Xtz\n8V9Civ+LUECZZAlyRXqkIFfLxnlWrFwghBS5WkLVOjg4wNvf/nY86UlPwm/+5m/iM5/5DJ761Kfi\nVa96Fd7znvfgS1/60sx1Gr/0pS/hmmuuwdOe9jQMBgO86lWvwsc+9rFKm7vvvhuve93rAADPfe5z\n8cQTT+Cxxx7DlVdeieuvvx4AsLe3h2uvvRZf//rXzzYAHexYdbzeIj8rRkesWgTdhJ1SipOTE4Rh\niP39fezu7i71QdA2YjVrXzjnGI/HOD09xe7uLvb3989sMztTXwgpHbtINtmQa1WpqlVlgiaHNUl9\nFy6A/n2QvvcZrqXGoYPSZNCHYMltfdro1Kri0B6Og+ZtFXdAeaJumhSbQr4M+yryqJTzqBIcdazl\n9jyJva4D3fnSESkvsjRDiOBZwT2s423hjzpyayPHttA+Op1I+3BdY4KI6wmML2mr71iE+ZmvYRab\nx4Mm9uPShGqJl+7WUdb6k44tfd8iFJBk4YBy+E6vF+Cvb71g7UuHZlCJ42AwwAte8AK87W1vw8//\n/M/jNa95DT7zmc/g5ptvxle/+lW88Y1vxDd8wzfg7rvvbnysRx99FFdffXXx91VXXYVHH33U2eaR\nRx6ptHnooYdw//3347nPfW7jPnTwx6q5zxrzqi4UsE2QiYOw/g7DEDs7OwvNo3LhvBMrUei33++f\nuWCy6McsmPz4N2W2w/1eTqho4RYn18MRqpUIE9LVrikcADV90VmjkwUZVAiISWPgG1KWn0ene58w\n9DC0q5gDSLWLso2qE0EaRUXIm7ZIrOkYOcH1LWhc7E/j/mbbF0/chVxdfa33Iaq0OyvJ0edN+eRW\nqW0Uh0AltFKEEBZkRCkAXPtbPfe6vutUOA0ZESqfzYHT5tpY9lnvBimDTifafVWKCueOfdm+p2VR\nYeH2J32PSt84BwgBjZLisiom2hwAUUhV3n5WiPszo4IslesYLY0UyppXWSHjAAADwGn291/fegER\n5fiW3zyauS++WGfFyoXj42McHBzg0qVLuHTpUqEkHR8fz/SM9B1H9Rkub3d6eopXvOIVeM973oO9\nvb3Gfejgj7bM69YRnWK1QphuRMKcIk3TRqYKi8B5fugwxnB6eorJZILRaIS9vb25FUNsSvLGb7my\nCIPhlFVIlQxVtaqu5EWbGlZZ5FGeIEdR4/AzGk69QgtldcAEl7rlsu1mUdgotE/dp8soYhaY+qwl\nBb7LcqIjEx5dCOAsNuc6+Blk2NU5877dhKnutNhMtUrH9dpoRfilqUaVBDox11ar9oEafwtWNz/D\nrYhGuSKqWZ/GfkqVDaWRBQVNaUWdkkMC5WXyS57Cip1lEz1hbDEIgIdfcWg9dgc3bMTx9PRUm2N1\ncHAwE6m5ePEiHn744eLvhx9+GFdddZW1zSOPPIKLFy8CyML0X/7yl+M1r3kNXvaylzU+fodmWLWq\ntM6KVUesWgQxUR+Px9jd3cXe3t7SrL9NOI+hgMIF6ejoCISQuRZMngXjt1wJAEWiNsRzTnIFBKqq\nlbys9rdnYjunaREmyBLpkxcGzRwBo9pnHsj23cyW3ItcWfK7ZHWrZnIhkdVZyUKWb6UWsU2t+7Tm\nzzRwu1sEZlWv1POqdaHzCNdr2h+eJpX9usiSruCvrX1tvSU0z7SuVh+qkmsl/59JoYH6fVXt2WVL\ndtXARQkPzfeXRon2fsk5R2oiTEJVchAqAEhThjSh1uLB1RrCEsHKwwELBJnLHc9nRgEh6AXA117e\nkauzwPa8NBGrWfHsZz8bDzzwAB566CHEcYyPfOQjuHz5cqXN5cuX8aEPfQgAcO+99+LChQt4ylOe\nAs45Xv/61+O6667DT/zET8ytTx0sWDX7WTKzIoS8hBDy54SQBwghP21o8958/VcIITfky7YJIfcR\nQv6IEPJnhJBfcA1tR6xaANmcAgD29/eX7lRnwnkjVrJKtbe3h9FotJBx9B2X49uenLXP39IWidsi\nzyoI9IYUnGdEKwiK8DFdH4rmOYHilIKlyZmUk3mSLZ5EjSbZdOr3Zp9GoXXi61LNZHKm7sdGbmzk\nzzTmpvFT91VTbKSJP42iejhdrcZTnhNlUK28TD6Uc8WTyIsgVwiP4XzL/Wdx7CQ+Ptedb24hjaK6\nFbsmJ081sgCqoX0+UPfbhCybc/ZM15C03HE70t2udMt8SZUJ4rZEqqwKQHb/E4sZK+3XBYIgyEkX\nEBCCYW+x5GoTQgFN3+/k5AQHBwdzO06/38cdd9yBF7/4xbjuuutw66234tprr8Wdd96JO++8EwBw\nyy234Fu/9VtxzTXX4LbbbsP73vc+AMAXv/hFfPjDH8bnPvc53HDDDbjhhhvwyU9+cm5961DHqrnP\nMnkVIaQH4A4ALwFwHYBXE0KuVdrcAuAazvklAG8C8P5snHgI4IWc8+sBPBPACwkhz7eNbZdjtUIQ\nQkApxWQyAWMMe3t7mEzc4U7LRJuIlYDuYShUqslkguFwiL29vYU+MH3G5fi2J4OQXKnK39AGvcy8\nIugLa+XqBEVMFFXlSpeHISamuhwspbP29R6QJ3Ymm3Hr9sI+fWvL+EapPFbWVs6hMbXT2ZoDAGes\nYg1fWUeFyqRfL/obDLe1k2nzflnlXFSNR/zDC035Uzr7dOt3qBUSPvt7NHFubGMvwJMIZNDsWlFz\npdTv7LJv50liNTGptFXytLRtHMpU4d7JqFfRYKFKF9e41m69tFCvWLJLuVaqzbqKNCzz9dT7pVCr\ndPfHNGH5OsN+dTWuLL9nOZ9KgNFqexEKyBjThmr3CfDgDx8iYQTX/vYTxmN1qCMLr9RfJ+PxGE9+\n8pPnerybb74ZN998c2XZbbfdVvn7jjvuqG33/Oc/H8zieNth/mjbvG7BeA6ABznnDwEAIeQuAD8I\n4KtSm8sAPggAnPP7CCEXCCFP4Zw/xjkXE/MtAD0Af287WKdYrRCcc5ycnKDf7+Pg4KAIV2vTBd8m\nYmUiSqt2TtTh8dd/YzY5IQS9flD0RyhVTA6fyVUpMUFRSZUMTmnm/uZQZBb5/c+iZNXClizXltzW\nVATYpabQKLS7uqm5OFK4VtOwPJ4mxgKspsm+MZ+mwbF1+/DJtTKpibplpnGWlxuVKtkKXVXdkkS7\n3BfOnLk8/LX4+4w5cE1VK5ZE3kSvqVolnP6qNut2xSnR5FWJzQWpMsGmUlXa5eGBNKUG9Sr7J1DC\nAYMgAGOseOssVKteAAwDYLvH8eAPz1e92gTFyoSTk5O5hgJ2OF9YdRHfRX40uAjgYenvR/JlrjZX\nAZniRQj5IwCPAfgc5/zPbGPbKVYrBCEEFy5cqC1rC5ERaFN/1GKUoujh9vb2Uk0+XOepP+iVb4wZ\nBwhHYFCWTJO1otYVYwWxKN5Y69SHJorEnMapVKIUZcJUPBjlJLqmPGiL+7oLzLI4tCoPvg56TUCj\n0EiAWRRp3RFNKo9NdartQ6NaFf3xOKe2sXCFbM6SW6UnaXpyVW6j5kpl37msg1W9JliaILA5BmpI\nuVzjSrQtnPWkgs1imXyuTURHlyOpA52OC3WqWiRYUjwrqhUvQomFaiUK+QY2t0/BTpDdw1W7dJlU\nqKRK2jRbbyNVUvHg7M/qvVErahFAhC4SQsCDTLUS5ApBpuxzzpELWujn/fl/fugCQgo86+5OvXLB\nRhw7YrXZaNG07sz4/b9O8fuPWV9g+X5b9cfCAYBzTgFcTwg5BPApQsgLOOefN+2kI1YrRv0h1K63\nZ23sD+cclFKcnp6CEIKDg4OVm3zIePwNT8ps1XskfytbrmOUFQSLpbSYMMmhfkVto3xipVp2y8gm\nc2biIU9aZTcuopmcnwXCPltrI8709zQWx06L7KKdw7baRGbK9QZCwShYTI1hbTIZquU02UiKQ9kw\n5UcVfycJgKTYf6V2lsaWncVRjZy5xqToqyZkbxbziawfHkTYQA4rx1eIua/TpJbsKbbn83RuFMW8\ntQWFp+OynIJEoLT7MSh2tvpTMsQEugzzU/qSUIlkKaTJEhpYrHc8B3yKC8t27EEv7wst3zALi3ZC\nUJAqQgh6+ZyI8myW0yMc2z2CP/nBC/iOj52NXK27YjWLK2CHDcEaMavvekoP3/WU8v767j+p3Tcf\nBXC19PfVyBQpW5ur8mUFOOdHhJD/A8CzAXze1J8uFHDFUG96bVOs2tYfzrP6XsfHxxgOh9jf318J\nqTKNS0Gq8g+TSIVMqnTgKS1vdpq4eGKIlS8L9WbheVxy+zMeKw8n1H3E+lngNElQxszUXiVjte+i\nU7eEyYApbNBipc7i+jrxty3c0PRd1dwcQYzMIXWGifWMLoGFnbqmyK9uzL2K7nrUp9KtdxlM6JUv\n935tNvdNCmbzNKnZofMkNp9bW/Fhh1W/uI4r9dcqdu3ltZuGcihs+XtIQolkS8u1Tn+VMMH6/SqJ\nzf3l3LBPCSZLdvW5xijLalnl/aUpA6Ws1lZWt8Q9lud96ZHsE5CMXG0FwJ+97AL+8KVdUeFZ0BGr\nzcYsphDn5aPBlwFcIoQ8jRCyBeBWAGoV7LsBvBYACCHPA/AE5/wxQsiTCCEX8uU7AG4CcL9tbDvF\nqmVoG5FpU3/SNC3UqrapVADw9z/6jblZBQpS1esRUJr9C6Co8yITLEY5Aq6fwOjecmeTsrx9mcQw\nt+8hkyursmWZtIlJb8+imMgTShaFCAzqVZGvohSR1YFFkVUFs+3DFsrF4tBqc1+z/i4KAetDAn0t\n84FsbFTzEp1a1iSk0KdgtE59kpeZVZbmqhVLIgQWowsWRcbro2ijs6/P+yirVjXjiRy2wr+q6YSM\ndHxaU1SLsELpuMY8uzi1h/R5QnbYk1UpHfFRVatsWVXdqNioazZwuQcKZUo1qwCk54qoDiwtIwRF\nKCCQxeb0AoAyQPBIoVwBWc2r+y9fwDgFnn9PMwXLZu6wDnApVoeHnZ39pqIt87plgHOeEkJuB/Ap\nZOYT/4Zz/lVCyG35+js55/cQQm4hhDwIYAzgR/LNvwnAB0lWjT0A8L9xzj9jO15HrFqGNhEZoB39\n4ZxjOp0iiiIEQYDt7e2Vkyp1XASpAiHo94NiEkI1kwpBqjjPQmGCIhzQpmYlZWjgDO5uPhNp7XEl\n5cA3fFAeFxpFzrCvfCPPfKpIMyFWwsYk0tHIjS9NgTR1OgWq+9URn1ng8/1n2m8U1SfFUVQhvWre\nWxMzCdFv2zYil8knpM+o6iVJhVypxF8l501UKx1sRNvmKGhSrWiUFCFwWbuSyFVIES3VnMpyVuYx\nyXlXjNXzpwRqLn8SQRJqlG7ynSbU+K7Gx45dQE+qRDdKckVYrk7J+WRSLi2QkSswIM3VK8ozoiWU\nLPSBP/jHF3Djx7vcKx+Mx+NOseqwMeCcfwLAJ5Rldyp/367Z7k8A/MMmx1rfVzXnBG0PBRRYVZ+S\nJMHR0REYYzg8PMzqnLQgJl4+T3/z2gsVUsWUMDZhuS4gwmJMEKFsmeqR1afSWitrxqHqvjXfn3cW\nHhUZne/0GzGwOPQuFuwzoWdp6g5Bs9WbEmGFDZz6nDWXjO5+kbMQsGzWoKvvVCtKrNSrksMkbQWU\nZ0ERUqjUoDK1k/+uOUCq30MpIs1qxhfmczyLIyVP08p2wi2y4j5JhZtf/dhquCBQVaZ8oBINagnF\nmwXqvceENKHakBnO7cWDfUgVTVmN6NWfc3l/UwaWhwXKNf6EWsU5B+WZWpWwTNziKAlVP+BFtnmf\nZPv98ksv4D/d4hceuMk5Vmmaou/IXe2wvlh1uN6SQwGXio5YtQxtI1areugwxjAejzEej7G7u4u9\nvb2CVLVpfDJSVeZSFf/S8s0yUHfvUvOlqEK0eJpqc6pmUavmBTnPg2kK1rrAoqkXwaKho11OPHXH\nV8MLjbtwTMyNuVhR2EgFA+qW4IXFeJPCsQ1s2WsEJk30REFDkH3zqGa1R3dBR65kIl93EDQ7DM6j\nj7acKZMiRqOkQqB4moJGbvVM3DvShFZ/a/n/k5hWiFORr5RQ7WxCtlaXV6caMifuqTKpUnfpY1Bh\nayOeJTRh+YdK69T/1HOvxJ1P5FkxDjCeq/358mGQ/TsgwO/fcgG/e/Pm5l/5PCfXmVR2cGDV7GeN\nmVX3uqJlaBtxAKoW58uAKPQ7GAxwcHBQiYFvy/gQQnDypitBCAERxX/zvKrMETDICgH3qiGBPSkU\niFEGEmQ5WEFAitpWtbA9Qw5AMbGTzgvXqliB1mt0HmFnLI4BzhoVDfYpLuvbjsWx1eJa3oea46KG\nw/muU0PECmMKS1FhE1RrcaCef1Qsn5NtvEqydGqTcx8++W5KGxqFtW3U8D4Wx+5cKt2YWYwmiMWK\n3aeob3V/FKRvyMNS3AdNELlHaU58bIY2LugUJMZ4+WLHcd/mvLx9uEMDzfvxIV1Zf8t2Nlt2OVyw\nh0y1YqikZCG7TXIAJCdZ5XF6QZZIAQp84eYLSBjBaQpc/szjyvdfb8UK0JOnNjxDO6wW3TWwOHSK\n1YpxHkIBl9UnxhhOT08xmUwwGo0wGo1am1h88sZvqpAqoMyHYFIoC6DPMzCFAtpyoXiSZuFTSex0\nH/NB6SYYa0O3mu2rWcFgGk7LPyzXFp1OjOuAjOSY1C0fVz+h2ugm2Kbis7Zjmib4xn0ZwhFNuUha\nhUrTVlV+TPvUq1Z+y9T1Pud/lhC+2j4ahAxWj+1XSDmdVK85TlNt+CuN03pon6RMVVQrg1Olilhy\n/JPvIXEo5fRp1KxsA/s9mnNJkVLamohRZRsDvJSsXKXSPe9qEPdTzpEyjpSV3U14mVsl7NcZF06B\nmXLVFzlXEOGCwFaPY68PfOr7r8DvfN8Vzv6uA3xI47qTyg5mrFpUWmPBqlOs2oZNJFac80KlGg6H\nODw8NN7w2zA+j/23hwDJ3/gwgPRIJZG8pzj+iXXCIbAwq7CQKEY5kOd7BIGwzXJ0bA4PSZlczaJo\nifyeYGsIW5Fg+VhOhcKjHpNL3VIJjGx3TaPIaD5Bo8hoc9+0L7p98TQBR2KslVXPS0oq56XuRujI\nBZvBRt9EhmyqVZEH5tNGVa2kv8U1YisAXdtvklSeri7VSr+PFMHAZFxhUa3yAr4ydKpSHJZOgK4y\nDGmsJzYmwiOWB4oJhKnGlQ5iG9kZUDdRd5EqmtTXm+7hhTGHtCwgeV4Vz98C56YVIhSQI8uzShkp\ntmM8I1eC14rttnocPQ4MCMGnvv8KRDQzwnjZp//O+h3WEevuhtjBjVXPo9YZ3S+rZWgDcVCxyD4J\nlSoMQ+zv72N3d9f6Fm3V4/P1V+4DBHnh3zzkTzdJUJ3qKNM6BALV/Cs18dtpw7zAN45nUbJqk3Gb\nKiUbOZgUHKEYWN7802ndXKDYr4twNDHkENvEoXu/Z3Cma0KCTKqVqxDxLMtsqtNZVKtZFVMW6w1C\nZNjWy+OsU/DSKKn9nmXTCaFMuYwdXKqVyH2S1WyuyalSUall1cQMI/9Nphryky3X2bSXx5qFVOnA\naFY0WNz3dXc0cZsLUKpRAam2zV3a0SOluUUvyN0Ec2TLOHoE2OkB2z3g4zd9I/7Di9ZPxXJZre/u\n7i65Rx1aBb7GnxWjU6xWjPMQCgjM/+0G5xxRFGE6nWJ7exvb29teYQmrHJ+vv3Ifva2gIFWc86Iv\n8ltnSlmhWnHOM0v1/G/5LTVY/kbZQ8GS4VJQeJKC5G/b52V2UShRaq0hiyqlWniXm2iIqEcNJq9a\nRoY8JE4ZOHUrX1nb6oTSZoOuKjJy+KFOtTL1zzfvzNYfnsReRFvusyBkPjlTop3tb1Mb9Tdba5PU\nlTkZpV27CN1MEFhUJzVPLbP9r+bFqee5vg+zamVTmWTVKg7TSl5lZR+STl66xgAAIABJREFUlbop\nNDiJU62yEEfu2lfy/pM4Le6vcl5VoRLxZu9oSvVLv5GLVBlDoUU+L8r5kVCn0lyJAkq1CkChVhFp\neU/sgAApAwYBELAyP4uRrBLgVr6/PoDf/t4rwHmmdL3ic9VcrPMIF7Ha29tbco86tAltnGeuCzpi\n1TK0kVjNOw6bUorxeAzOOfb398+F5evXX7kP0iP/P3vvHmTbVdWN/ubeu7vP6e5zDgnKK8HiIlQR\nrxhCNIEQkijfJyTmI7nwgeAVuEgkBSKPEkUpFC1LLUopPyEUJBiQlwEfvJOQTxDykJvw9l68gAFB\n8yAg+uXknO7eez3mvH+sPdYac6wx55p7d/fpfU7WqOrqvdd8rrX3Xmv+5m+M3wAcLVhQC1QYJlZB\n4Ih2uOXip15QdLBy0srSYjiaAjdNTUu0d3m1wK8XJzuUH4kWtloy19D3thK4cDoYsNwlbwxYW4Mf\nmZ+K6hAAiyn3hUQE7GTSKiOxCa2Mn8NgeXmm2LZQIuAguFIT3OqAJzXnVSpg4vW11zttncmngRbL\nmZqXap55p7CDfMNkFuMJwp3VmesiL717BQdu1toaXMn8VQP2ur63MJTkHZfzKvx7USrgisVcpbBU\nXuJh+KIV0nKWFBiowBW95eBLe00uhJTzCmjGGRg3BWwGy4NqnOXBdCwLfOhnTjphAJZmR44c6XNY\n3c9twZaZJ5Qt/or2fmaLCqx2Yk7OOYzHY4zHY+zfvx8rKyszg7ZK2jzNxWSn7I5nrmG0PKwWMQZe\nwk4zMFXeFeNajBPVGwwH9eJGAq3YrrOzFvWayJh6sVO7zMxw6WyWtXxsBkvLcyelrQFWiDVQvi/J\nYKAjpqqcjFtJgmexmLqeVHbzEgFnmZrEeVbw0vQtWBoxL8kmdea3EvFXsfmFjs1jkh3SVA1T4ppa\nin0BdcS6vMg911AtT5Y/r4aBIlc+nrCXNiw4E1UoMukELDj4kcxUCEC1zkGAI34/yANufV1iEiFL\nVcALsVFFblv3HN5nF6iSgCo4vuiGGCvtmEETY2XkcQMUaMBVM2nUsVpko2kslwGAwTQJMYAP/sxJ\nteLgsz9zfIGsLsaqB1b3b1u0deaJZH2M1R5b6Ma3SF/6nQBWRVHgvvvuQ57nOHjwYLLr327MZRa7\n4xmrzS412xat3Wps4+bHE1uS8R3jetGkSaIT01XYaALhudlDpZmtF+7xOCoXc/ebqhRGjX1e0Tga\ntkjWYp68HFUiSbDmvhezaI6rORLs2mzSYrNsnotEwCzJ7gx5qaj/9rF4fqmWe12CG1+rv1aeqITP\nW7QL1efXI0XZb65YvzwLKjImtY8k8pYWA1JUlmdlq88QUPJzWdm6rpbjqshLVSGwFPXJeI4r/vvU\nhDJSbrdFVkbvy12gyhhMFQD9PmiBwvef6GU5zWFFroCkFui9do37H+C/JlsaOIym+a9GponTGg2a\n10MD/M1Pn4QPXHBixGL1jFVvsCfw3x5bz1gtmBnTxO8sihTqdsCMcw5bW1uYTCZYXV3F8vLywpxX\nl93xjFXAmMoFEKh3OrX50+41Z62ssqChugABLePFW6kM1gzXazvXdmZFQA6Y8srdr8u9y9kSjvL3\ndOaoSstjFY5/6shxNRm3yusYqZC7HmPTZL6qUJxYqK+UuLJ5TLsmGohyRe59XgSAJEsUY45qcN7B\nLtXjjZaiIKqOpaoVA/1+efwgUAGH4VLjbllkRe0yq89XgN/SeaxVdaz6LWuAJxvnHqNlSxv9nafk\nqNJYq3lZKW6amIZzrma+JUOm1aX7CQlcqK6BAdVCII2lygUgla6BPHcVAGSWsYyuec3ZKnpNsVbU\nnliswfRePjQOEg8b+AyXE///6oKT4AD8/IIzWLE1xJEjR3Dw4MFjPKPeFskWafP+RLOesVpAWzR3\nwHnnk+c5Dh8+jLIscejQoblc/3ZqLrMagarBwEylaU29Vaop/tXxEIJtqt0BBwZFYVEU7bYqg9Vx\nmXYbm86sBjj9TFyeJTM+drIVLCN2KpiDirNbMbatIyYqluNKAqcmEfDsDEhqrqWq/7F6DdU8TIFz\n305OsrqPyJy1MslmaexWSx4+z2a6NtxKxU0vxbTbR7YVUQ1Ufu/BOTFmStqE56JKZMK8XFaTQj2e\nT/QcV/w+GVIUZJUbICaqFrnPRvHrJ93/fNXA2UFVsJ6tWKjCVfFR3Lg6IOHEql712qJa6PB7JoG3\nWpLdVEqBZspaVVteqI8Np0zWYMpkDU0FsBaZwepdAXvrbW+sZ6z22LQb36IBK2C23Q3nHDY3N5Fl\nGdbW1rC0tLRjLNWxuDbfuXQ/hsOp+t/QYDgcVLu7cmdbUfWScVb17jADWPNaqnvgaGmIsigxpFw7\noSETLiN3oxosz5BLKDHuKEXEoNzaCMZE1eMxZkPKWnPma1bxiRBjZgO5r4KslYz3mQIMqq+q4LHr\nFwMoVfyc+G5mk9Y10661xjSFjmnntBumxUrx72oXa1UWbaEXzhx5vw1ATeA9i8WYqc4cVRSvxe4l\nKYp/ZCGJ964cVzKpeTCualLW269yoU5MlSq20wGqugCVMUA2/RlzTEje2APjYJ0/LpVR1xzzkZCF\ndQ0DZsyUuWLlZCNTgTNvTHrDxisd8IELTqrbPufGxWaxyI4ePYoHPehBez2N3vbQFm2NeSJZz1gt\ngC265PosoIhYKuccDh06tCuuf7t5bSSocqWDta7a4Zw+4SsBjbYbDYEqEquI7RJrCyeqT7msyqIK\ngJe5rbqMFkllUVZ/edmZYyfFykk+E0tgswnKcTd75fIMtqNejAWr2a0YwxJhpuYtC1k5GbeAEhCe\nXzlDTNc88wEaxqz+z4HZnKBJutVpx8qEvEoy95ImGCHNyXHycrYcTsr4/DeWjaXLoPV+Q7TJoQGY\nicJ+cQA1qznralc8j5FKyHHF75XcZc87rt0beHfKrSfm/tflxtgFqjLbgCrAj68CeIxV85/YLJ4U\nmOe+wvT9gB0jNqp+P3DecWKuiKUaGNbX9D/FX1G/15x/Eq45fzFYrC5XwF5u/f5tzp24f3ttPbBa\nQFtEYNU1H0r0u7GxgdXVVayvr+9KZvfdjM/6l0v2Vw9MV+WncqXDYDSAmz6tSQGQzFrXWig5Rd7Y\ni7sSroIkbkHHyqKtvBWzWa4HAaztAq0WwOr4bhDrFUr+S0bua+EkwQkgTbBVnKHqAlBB+XYlEbAr\nC1+afBuJgMNzCiXSVVwCFffEWUQ45gVSKeUcXJVZkfTdk3UkA9K1eJebERIIpbipzcJkxVz7QmXZ\nWDBz1s0EwELXgLsMphj/+XqufFl73o67DGptmEy7ZimgSjO6hea2EawAfGU/6Q6ogSvrGpxIc6xj\n3qcMGJXHtrI4SONzJLfE959/Et533mIALM2OHj3ax1jd322v0c8JjKx6YLWgdjwBqyzLcPjwYRhj\napZqr+Yyr/3LJfurh6IxMNMEwACm4KpiqEgBUIuhAuDlmOFWAye+S6zEW8VsN/AkMVrzBsprbIQE\nNnVdufAPfIYpan7lViQ2qzOmqplHS8UvEjsVjmUKgZ/A8TwL5quq5+W5+U0UZb4Z3BkVcKXFNMnP\n0uZF0jgprFXMiC2KsU1zbwKI71hKXFOIGS7yshVbKYER0JwHH0v+vjhoSplTpQTob8Zor10AmHHB\nCs+lkh2XP8eWdHrCrSrGqueli4Kq3FZ/sdscgarctmvVgqs0F9f8t9P/dI5cDIMYqqqPyjNhwI4T\nUCLmasDKCVxx1orqUVzWXgKsPsaqt5jtNfY5gXFVD6wWwY4HV0BtPtZaHDlyBJubm1hfX8fa2tqu\nK/7txrUhUDUwBoNhxUpV7n+mBlUyloqsLG1rwUXztKXV5xqIq0upl2LzNCvysv4jS7nOZVYEF8XS\nPanMiiTXMF5HyqjXdQIgyBVlECBRXzGZcWo7WyxWHFy1AFwm46mKznlJ4+dPoI/mLvuZVxyCG4Gl\nWYCUZKq8sh1grSR4kQv7LvfZsigx2Wpfm4KBit1irbTNDCmNHmOtUjZDGin2wGZHgB7KI4xXmVt1\n4aLNh+p1sVRyevL2lVuD3JqgS2A9NwfkromN8tisGjxN/7Njzk2TCFsDpwAx75yg319l//LYNXsA\nsLqAVc9Y3b/NOXfC/u219cBqAW3RgZVzDpPJBIcPH8ZwOMShQ4ewtJQubLBI9vX/1oAq66Z5qAwJ\nVjRSynyRU8dQTa/JUMovK3motJgq7RgHaXWMVFH6cVfTv+0G3YdMAiygexeoiAAsaXKR7ZQFaRIA\nm0wiboPtvFJeeQK4ardJAyh+UuFQX7rroFY/5VrU7ZW5y8+lzEu1T+1YCEi1ZMs73mv9S+BUZEUr\nvkoDVzFQEQNTQYAhN0siboKaImjIYmUukbXyNjp4MuRALqtQrJWf44q9LPl9PTgNAEDpxWix4zXr\n1e4gK8KdEkull+nslLxlls7vh8dT8ff8mIzNqubutzFT1mkA38WP2Ckqo3rEVHXZ+847Ce9dABfB\nHlj15k7gv722XhVwAW2R8zyVZYmNjQ0453DgwAGMRsf2K7RToPMrF61i37CS2K3WHA5D8uFAxcYN\nlHw41QJFAQKlrYFS7PNT1QX5wsqY2kWQuon1F1tIjpa2t29Ci7rRUlv9jkx+FkVWYrTcri8/smKS\nY7TSBuN8AVhmRetateYY6IfaD5fTvp8uIeYGwDQ3ln9dbVECKGdSTdwJI9Zqu/cLzQ0w9l6zIi+j\n3xOtTpGX0ZxTVR0b/R6HQElZx1JZbwwtb5Wco7Rs7H8Py4AwDbXlGya8P1II1Ni60gNQjUuxJpLT\nxfbx9nlWthQAgUrtT/vekCiFtdaLkU2JSZPW5frX2V5x+QOaHFWE2Qb1PXz6HqhV/+i+U1r/rk1T\n43VGxqGY8mCO1aekw/K1NAmurKsOGlRjUFnpgPee1ygJPu/m3VES7BKv6F0B7982h45Ob4nWM1YL\nYMeDK6C1FuPxGPfddx+WlpZw8ODBYw6quG3n+nBQ1eQnqdxA3FQBEKh2c2lHdzDwXQJ5LJXmCkh1\niL3iwfTasVbbHcDWRW5bf9JSLqPGYGlGi80iK6OqYbTzXkzyTgW4VqC8tqCd9qGBoxDbY0sXZYI8\nd0QpnBDqM8tbua/4/FLql4X1+q8BQqa74mnfH23hrc1Zc83Uron22Xd9HyrXvAR3vxnd9zSTLnNa\nn9p3n5/DLKxVa/xEZipWpt1DuoQsvFxWkd9bq19Rl+5xRVZ69wNLv1P+WbMKhXL/ovtyHmHCMhvf\nVc4CgIq3l0SYxmQVth1bBSiCFt78mzpULuOs6DWPx5LtNTPsP7U3Bnj3k0/Cu598bFms8XiM/fv3\nH9Mxe1ss2+s4qN3822vrgdUC2qIBK2srt7csy3Dw4EHs379/z1i17Y77pQtXsTxwnoKUXLc42+z0\nccl1WYcvbAYCaJXMHTCUq0w5mHwe816HGMjipiUETQVY1D61bqgeAbAUFcMYQCuzIhyrlRUt4ESf\n9SwueGStuLKiAZFAGxjFAKg218464lz4wrdIVORLAU2ztqOyqBtfsF/rvZaL+ZT4Jb++S3ajrcEN\nq1/ktk4ErI1Zf38UkKgJXpBxcBUCZLH4J/7IcNZFXfRix7v67lq5TJRrS01Cqn9kXaAqielSpjcQ\nYIrHVwEVuCqmqoASXFGb2FnzeKoQCAvdsqnOTgOsGGMFYFdUe3s7fsyewH97bf0vawFtUYCVcw5b\nW1s4evQoAODAgQMYKklRj7XNe32+dGHDVNGD1jqoAcdAtWBzpYNhbkCh3WNarFG5Fj+lKQZ24aPd\niqMC9EVqWrt0gFXkZXQ3nYO2LpMLb/lZRBf2c+bdCYGZWv0tAmSkzaqWlxqzFhJCmLdtar0ksBRg\nfjy2KMBadYF/3k8LXLX6bMu1y9/WZCzZwGPDWqUwgjElwFl+wyFgVrDj/NaaZ/pxAoHyzGLASZY5\nr8xEQRWPowrVIvEKMnlv5a54pBYIcGbKeWwW1bFoQBLvhwMmirfqulsT4OKgi5ftFMCKPR8XYW3R\n296bdSfun2bGmKcZY75ujLndGPOaQJ03Tcv/0RhzxvTYw40xnzbG/JMx5qvGmJd3XdseWC2ALaIr\nYFEUuO+++1AUxcIFuc5zfTiocqh+fBxgVbt7TX2KhyBzCsCpXP1c9Gmq7RgG40JqUQrfTVATrtDb\nzymbPu1zVtn1fFIkMy4pfafk30llUzQAPC+4CrmMhYBPaJwQKJ+FtZrlM1JdAjuO0XcoBTRp5Rro\nTslB1eUSKFnWeRJmazab6p9gI8mFTovLUr7LdQ6tCAiLsVYa0CxzqwpQtI+HX9efj2CpQ9c4L523\neNGuoGypsUjUdh6WyrAyTbyirjetWLiqjvy4pVsgiVhYpS8OhugZ4hhIc64BWzTHEIiSc9A22N71\n5JPwrm0CrBBjZYyZ2+uhtxPD3An8J80YMwRwBYCnAfgxAM81xpwm6lwE4FHOuUcDeDGAt06LcgCv\ncs797wCeAOBXZFtpvXjFAtpeAitiqSaTCVZXV7G8vFzfhLtcCxbRPvvUVewbVA+30plqVxLA0qB6\nIPKdSAB1HJUEVR5rNXXwN5K8E5fGlg4wzec4GjQNaDFTX88Zryst0nbq46DvW5GXcM51ChF4cwkI\nVrTqzSFwwI2rn8k6yTLVWel9tnJsWdaVZyg03yIrVYaS1/fd9Nr1y8J6fXPQM1oa+u3zcsdznWmg\nad5+hqOEz71DyEKa5hLIP/uisF6fZRGeB4GWsnQYTn/rdL68TYxFk5sx3EKsVf07DgheeH2w+5Am\nakHWykFVH58BlJe2vp3x+35WNBtQku0PsVUTG1bMCwlUVGXxOYbKSbyiJeNuKvDD81gBjQsgmecK\n6KhOs2CzUwBFF2gwBVbUPwEvaW5ahwo5g+bNU7R757knAwBeeMt/Kr3qdjw+q3vrbRftLADfdM59\nBwCMMe8HcAmAr7E6TwfwLgBwzt1mjHmAMebBzrl7ANwzPX7UGPM1AA8TbT3rgdUC2l4BqzzPsbGx\ngdFohEOHDi2sD3bq9fnsU1exMmiSOBKocpiCKlRqUbT20vJV8YWSLRqlLKMoi9GO9oCYLDFnWgim\nqP2llGsm2YGuBW3IUhQBuZGL0WhpGP1smnqDYKgGyUbH1OA0EEQmF7gtN7GswCigFhgqK3IdKMWs\nzEsM2fWjeaQATD6uCtzytqqbVNCj79tQADmtz1SgLlX25PvYnP1+4mBLAzWyTZKqoMK6TLYyr59Z\nc1WFvnfSytJ6qRhSy/h9iBT+tJxTHECFQBcdJ6l0+g7Twlvek7juuANUcKXZuGyDJw5uJAgDgEnZ\nzk1FFgNVuQuHeeV2umkWaE/gJ/SRS/DFmSvuCmgZgCK2SuuH6vBYXjm0ES9kX4Pp5tw7zz25bvtL\nM4AsaZPJ5LhNj9Lbztn9TBXwFAB3sPd3Ajg7oc6pAL5HB4wxjwBwBoDbYoMt5sr5fmZ77QronMPG\nxgaOHj2K1dVVrK+vt0DVIrgnkqXM5banVaCqUf5zGE3dAIfGD2LmD1mZrwqY7oQH3GKcc5VQhXaX\nUhYNXQvXnd5k9HNhzc44hNTdunbg63pB8JQSPxOPW4ntwHfFJ9UxUh2MlByTGwdKwGzuaalqfrz/\nnbQUl71Uk8wZ/6/1HYy7miPer0vIoivJsNpn6cc9SfdIbpmIy7Kl7lKr5Zjyc1S56Vjxa8Dd+6xt\n1+1yK/WUBPn4bGohV0VS+vOUAx0wCQwZU/+blPMxVeRSGLtPhtwCySSoGhinlnNhC24ElhyrI+dD\nLoEO7bgPnvsqdrvXyun9O849Ge+YMlma9VLrvXXZXrvr7eZf4HRTTP5o6nbGmHUAfwPgFc65o7FO\nesZqAe1Ygpgsy7C5uYmlpaUoS3W8AKsb/+sq9g2nwcRoQJV1Bm7KWNHuKT13hlNwJUmoWtVvuq1K\n18Y5B1e7A/qNVNGKXUJTszZzzl/MEauQ8rmWRSXFrDERrVxWiWxXnhVYmrJDwfijjjxGZcR9r8iK\nKLsQAlUh1ooWvZrbo8Yg0fyGgWs2S33N1U9nntrXqwYXc7qbyjE0lqqrj6pdqTJQXeIXw9GwBjdx\nd74ZXN1YP3X+qUQmqs2IhnNjpTJTsbJ8XLTuy/SZynxT4fZpnz2Bpzr2FNV9NBNghYitzDYrEc5K\naW6BVM5BVaiNnK0Wo8VzUHW5BXLZdX68fj99RvDkwbzewPhjELji7oLk1VgzU9SHEcCK10GbATNK\nfZpj1X/DKIasC1itr69HWvd2fzDrZlxALLB98X85fPF/RdcxdwF4OHv/cFSMVKzOqdNjMMYsAfhb\nAO91zn24az49sFpAOxYgxlqLzc1NFEWBtbW1TteARQJWIbvxv05d/9AwVdUDymBp4FA6YDS9lxQO\nWGJsFV8XhRY8tJNb57KKJBotc1uXG7YjSgvSCki0r2ct8x7oel7XPs0adysWT9bxGddtEhahMrZG\nY7lIdSzuFmY7k7oG47IiboExt64uUDbLPErFjbAGadP6fF5lXra+AGVRinirsNhDkds2CBPxWtSn\nvO4hN0EZ09U6R6VMF6noELYobIvm1Np4DEsrCbD/ufLyVPAlwVI2zlvfIz1JMLkQG3bMZ6bMwKjX\nKx8XalJywAdQmpAOteffM8+1WbgXlpYW6Q4DTWCHAR7NzY8bgS/ZTisfl6YFmrradFkX+a0lAwYY\n6BJxXqF6GkByaLsCcoAkb/Hyk5PuhfK4E3UrIObwgm0kFT569OjCCVL1duztRHIFPOMBBmc8oPkd\nv/3brZvCFwA8eurKdzeAnwfwXFHnowBeBuD9xpgnALjXOfc9Uy3Krgbw/znn/kfKfHpgtQAW2lna\njQBUyke1ubmJlZUVHDp0KGmMRQJWci43/MwaVgYO+4bVw4yU/0pX+dsPTAWqDBpmaiBYKg1gAdUD\n05UuGl9jjKldBR3Lf6XWq5/yej9dFnJlmkVsQloKwyQ/+hBzkMpeSTcmvqDXF6zxuJ1QubUO1obb\n8naSweKMmtcmK1tAr8slbScsBnpmtVnd/iQjN49MP7XrYru4gMQs/XILAR+/TSlirSpAVrNBESZK\nWqyuLRwGo0BZB2uluSDXwjc1aGKgy7pOIYy8dCpQGheudf9rzQkNa8UBFwdCGlvlEBeq0Np4DFag\naSw8LqRECFSCFdrjjEAUgSstEbEm6SzBGD1rZDuNldIAFUdWVPz8GcBU7wrYW5ctxmru2JhzrjDG\nvAzADQCGAK52zn3NGHP5tPxK59x1xpiLjDHfBLAB4IXT5k8C8IsA/h9jzJenx37LOfeJ0Hg9sFpA\n2y0VPmstNjY2YK3FgQMHMBrN9vEvIrD61FMqlopAlXOAM40bYO32N21LoIuMgyvJWtFY3OpdX+4O\nWLNMGpja3rmmGA9Cp+vSUs1L+Og0Bku1aWe0wAsqobExi7zsZLlSwVMsviu0SNXKYiqDZCFwlWcl\nlgIugdocYiIUQNuFdFaBi7aQRRoIk652fE4p4/L+NDGJLiBFDE+sjtbHrEIWlFJAgp9Z3AdbTJhw\n8+MxgQS0SHSCgyvJTHEAZQubxFpJU1kxcmVm49QMFmOJrHM168Pvh9bp4hPjgPsf0Einy7glDqok\nCEvxUmSaGlW76emSnLm8JYRAlTHNXCQYIgsKW6ANtIAGaEpXQMk6SRVAI45rbNjztsFMhezo0aM9\nsOrthGKsUsw5dz2A68WxK8X7lyntbsGMehQ9sFoA0xfkO8cQOecwmUywtbWFlZUVrK+vzwzYFk26\n9VNPe2Cdl6rOOzJdFBCoAuihazA01S6tQzimSrJWNWBiLjR2+pnQMfWz69r27SregUutxVJppn3H\najW5hDgaYoQ6x7EORYA56gJgnN3qAmgxQNJVFpSvDuXzCYCrEAsRZNVKiwGT4o8lt9VAlJRlj1kI\nXEnT1P9SxuDtwvnWwmCrzt0mWKtZ3flC3xPJLHWp/NnSqb8RbQ4xUDRLXSqTSn6A/1kRgKLvi+bS\nJy1nqMEHV/7Cf2gaxij1djRmKn92mtoC0JmqLlc/zb2vjutSPn4CVzzxb7tPfeOLVALpuaD1W9en\nuRNTNy2rBS+Uvk1CuWNj/cKN/7nt521sU7YHVr0B9y/G6lhbD6wW1HYKWJVliY2NDTjn5mKpdno+\n27UPnreGtRGwPHS1uhJ52ZCLH3cDJCvZg16yVBrIIrPOYUALjMizrrXYreWrq+NdeZ5s6TAMuAtt\n1/giMDVGqxK6oDigtMVinpWddRuhAP1cYwCM91G7783oNphaxpXRYkyBBq5saWFLqH2FRC5mmWuX\nxLnMdxUDarMYH4Or/3VLq1fz7YrRShXEaNpIMQwBBgPCETWbpMwnG+dR4N7FWnl9bRVemS2cquSn\nAShu3L0v6jrI4qWy3IKG5iBGu9eFVP3a/euufxWz1WbCqr6JwWr3lyls2MTGt4YlqJKAEGgLU/Ay\nzUKCFWQOurseZ6+0HFa8DXcFBKtD7Z71qX9HWZb183owGGA4HHr/Z7EYsLrvvvt6YNXb/Y6xOpbW\nA6sFMQlctgtknHMYj8cYj8fYt28f9u3bt61dsL0GVn/15DWsDIDVYeVmQuIUoym4WiLWCvoigsQr\n+KJCe9gODVBYYDgIuz56AeJlG3WZ+hDbaVY0gDXmQXTlz40xAfSa97Fddb+QkYSzplbXqpsAxiqW\nqztPlcpuMfe9GNMQK48lAo657IWu2bzxRin9z5L4N5ifqiPfVegzS81R1ZZW1+KC2mIb7bg9UUdI\nuen9lqo7V9f43GJgiX63PEYq28pbbBP9RiQTFVUFjLBWmpIfnQMHV1luk1zpgAbIhDaSOEjZKps6\nHERVrJRrHdeMC1V0gSePPUO7PCrBrpRxNcD62FT5j1voayHbS+bKujYAMwZe/iwOsqgPakv2859p\nXP1o09O5CoCXZYmiKJBlGQC0gNa8z/ONjQ089KEPnattbyeO7XwDDJNEAAAgAElEQVQUcG9kPbBa\nUNsOkCmKAhsbGzDG4ODBgxgOt68kt1fA6v3nrmF5AKwNp0p/A1fnoRqgEauQoIovNshFRIIqGVuV\n2yo+ixvtANMzrLSultfVnmv6sfQHYKwqXxxKVblUo4/QZ7ESE57mJZxzSWMWmS4b7tXpkFLPJkUc\noHUlAp6TuZJ5fEhwpFbHSxwnlFS4K94qBUmFGJ5ZgFis79j7FFe8JJGKgPx6zFJjqYCKFaXPqswt\nhh3fpZDkf5e1vi8BwCRFJ4CGrQLawhPzmHWuXtyX0w0iIKzsNy7b4EgTkqiO63Oj4xqIksxW7PQm\nc6z0UpioWJkWZ1U43U1Ki+UicGUD/UmGCgCe/Zl43JQxBsPhsH5uO+em+RIrRivPczjnPKA1HA5b\nm2whluvIkSO9KmBvSRtSvc1ns/HLvR0zmwfIOOewubmJI0eOYGVlBQcOHNgRUDXvfLZj7z93DX/1\n5DXsHwIrA9RufwSoare/6aZ2nV8FzcPboHrgjQaNC6B82JauAlS5ZS6F7FdRWIdiKk9cWl2aWFvJ\ndoGpnYpZo0SvVSLf+ZXavOD3jo+Z6nYtRMkdMqbO1pXQtMhtNFFw3tmeFN7S5MBpzK7+Uo/Lc6fP\nKDQvDdRIUQRe1pkgt7Bq4mHtHLVrncI+pZiWkFgzL5Fwwnc6JdG0ZtlWPIF0GyxNwTVjpuq62rVk\n38tQwl1A/w1xZqqerxjDWlfHS8V+hnxoXq90DYDizWUdsrGXe8qox3k/48BHTeCJn01m22ITVE73\nZmm5q/6C8VSBa0IKsdz4rZjc+0J3Z4e2+JG8X9KzStol//P7uOR/fh95niPPc5RlqbqGSjPGYDAY\nYGlpCfv27cPa2pqXIiXLMmxsbGBzcxOTyaQGXiHb6RirT3ziE3jMYx6DRz/60XjDG96g1nn5y1+O\nRz/60Tj99NPx5S9/eaa2ve2O2RP4b6+tZ6wWxLbrCkgs1WAwiCb63Y4dK2D1/nPXsDSogA4l8q3c\n/hoXQAJPdb4qNMCI56saDRwKa2pwJVkr7QFKD/KYBkUXvvIWuNOC2I75ThlfiFJcy6zJXD3WIPCZ\nF3nlgkV9h74aZV5O3f7CMVGUFDcKwLTEt9MVUp6VLXluPk6X9LkOuuJsmj7HtgBGOUXzWl8xwYyd\nmI83j+k1lvmuktp2fIdCYiexdvRdS2GpuuYTGkcq80nWSr6XTFM2LpLytQHt2KcY+yTLZI6pkMVj\nQSn5bvWeh2umxFARsyRV/aRKIBen0BQDgTbjRX1r4Cl2dbvirbR+YhLrMbl3Te2PXPk05ssY341Q\nuv2RPfum+/y5Wuv9AVUcdNVnBaBSnt3GGIxGo6D7ILFbZVliMBjUYGppaWlHgVVZlnjZy16GT37y\nkzjllFPwUz/1U3j605+O0047ra5z3XXX4Zvf/CZuv/123HbbbXjJS16CW2+9Naltb70dj9YDqwW2\nFCBDLFWWZVhdXcXy8vKuKPgdC1XA95+7hoGpRCcIPDVAylcAhKvqla4RsCicv6AoHQD2MC2sARSA\nVZcHXFXoGGerKMHmdDlUveZxVka+8He25eUcLg1hi7i70qwmd/tTcTExHNKVL6Qg2FrUBlTUYi6E\nEoBplk+KiPteOPeRXPRy0BWXaLdtifbSAmVzbXYjXxWBoJT5aMAkBDS0xMOtOh2JiGNjpIhUhAU5\nSu+1JkoRY7xSxq7noLCcXcwp0LBWzXs/Toy+Z6ooRlZgKICXtslALFQNZmybYQEa8MK/8iEApYEj\nrX3IJmVCJTEvPhYd1756NWvm/PIatEGJt1Kuh0Xc9S8GqmL7CxrODbkRcnB14bV3YzgcIs9zT3xC\nAidrbQ2KODCiupR6pQtsSffBjY0NLC8vV/MtS7z5zW/GlVdeicc97nFYXV3Fl7/8ZfzIj/wIDh06\nFO23yz73uc/hUY96FB7xiEcAAJ7znOfgIx/5iAeOPvrRj+IFL3gBAODss8/Gvffei3vuuQff/va3\nO9v2tnvWuwLunvWugAtqKYxVnuc4fPgwnHM4dOgQVlZWdg0A7bYrIIGq5UHzR25/HFSR2x8l+B1N\nwRWBKlJekru7GmtFsVchEQsyckcht8CiwwWu6yPQygnMlLlV/7Zj5DIWWnSGPlfNhaxpI/oP1JUg\nJtiJqBNyMwy73Nnownuny8q8nNm9UHPb4/W9GDrFDa7t5ld6/3l57PPW+ug6h1oGXYnz0+rx97K/\nttiFMl6HIIZ0kaRjse9s1a+NvicXPzouFR1tbPUurOUGGrlvxNxq+ZCpMUWEAbW4Je6+1+Xul1uj\nugpmNuxCCHE8Z+CJm/z6UHnodkfuf2qZNS1hCjoeAlWlC4/Fnwux27m8lz/rxvvw3z9zuBaLyrIM\nR44cwZEjR+oN0LIs63suxUgtLS1hZWUFy8vLWF5erpkoAltZlm3LffD1r389vvrVr+JXf/VXcfTo\nUVx11VU45ZRTcPrpp+OlL30p3ve+9+Ff//VfO/uVdtddd+HhD394/f7UU0/FXXfdlVTn7rvv7mzb\n2+4ZJbo+Ef/22nrGakFMAiJjTPAGaq3F1tYW8jyvWapjMb/dAFaSpSJhCud8sQrnWMZ6NMIVBKCc\na/vWyrxUQAWw6Dk7ND7Q4rK99OOMMVjcdpvR08DVPOxWZ44q9hE75+pFcFeOqmqO3YIVtIiOuX+l\nKP6ZSKLUmOJfTCmwEqZIZ9tC7l6hvmKCE9vJQ1X13S3jTiCBrj0HZvLz0PNddQMpzWTuqBjbVb/v\nEJtINSl5rlkKWxUyKaAyyUqMWu6gCoM1RT78MvAcUzKXFDeu2Ef1QjFNsr+QESvFWaZxaQLKgLo4\nRarrHlDJpqsS7Aqp2uUyyIFTV/4sspDaHy/j1uUW+MzP3Mfe6256RVGgKAqMx2MAqBmm0WhUi08Q\nM8Vjo2Pug8RqSUZLk1s/+eSTceGFF+KKK67Apz71KTjn8JWvfAX/8A//gA996EO44YYb8O53vzt4\nzTRLfe4tQqqW3nxbhFikE9V6YLWgFrphUaDq8vIyDh06dMwS9+4GsCJQRYDKoHmAmimoIpDFA4IH\nqB6GEoSRaYp/QAWqmtgs/1wKB9CjTLui2qKk88rPpAY4++fIwVbXIrS1W5wAmLiRSERnnqqsCPbL\nvz9l4SdwlTv2XSAtFpsTAyoxJcEYYFPnMHULHClugaG+4mp+3W5+VHfWZL0pJpmjlJxbWrwT0K00\nmZRImIErTfa8JW1es77+d8eTTy8ojxr/DoikwS3Zd+uxTzIPVizJsMZaDQOup7n1c+957TqAkVZv\nszTefa5iYQhANQBkszBJfccsyCQRgJm+5y5/XSqB3EKuhCHwFGOppPHkwppZZdOOGwdVmkk3PQCe\n2994PEZZli2gleo+SH2REmDXs9pai9FoBGMMzjrrLJx11ll41ateFT2HkJ1yyim444476vd33HEH\nTj311GidO++8E6eeeiryPO9s29vuWY91d896YLUgpjFW/OZorcXm5iaKosD6+nqtCHQs57eTwIpA\nFUmkG0xd+eAzV/Qe8AEUKQISugmBKY21qo6baT9ODVymMaRxFxEOAukuNeCO9oz+oYWdLWdPhJpi\ns4GsZl6NYEWqwIVNklzvWvzHEgFrDJjTEqtOgYdWFhq/yqEVkVoPxjelC0109TVTHxFwJReaIZap\nzQ5prn66+58WbzUbWCPw4YJJoeVcy5DeN687/b7HckFJZb6hANQhcNXItTflhXUtJkpaToqPrG4d\nM8WmmLEbTmEr1kpjnDaKNtDSclFtFGEAVTrT2kTSTMZh0RT5cQeoghUc9HB2KXR8XDaveT/cZZDa\ncYzbjsOaDVTlNgzkYqAK0JMOdwGqmBFYouc4yalT3qqiKGo3QQ60NFZLAi2K0SqKoq7P2+3kZuxP\n/uRP4vbbb8d3vvMdPOxhD8MHPvABXHPNNV6dpz/96bjiiivwnOc8B7feeise8IAH4MEPfjAe+MAH\ndrbtbfesZ6x2z3pgtaBGQMY5hyzLsLm5iZWVlWPKUu2GEaAidooYq4EAVc4Blr3W1P+GBupOrgRT\nfGEQ2vmlY1QkGSzpGjgLNDJox78A8gE3XYAlqJ11GS06Z3GlKgsL2PQ2KawJsVyxc0gRtYgtyMsi\nJj4xWxnFzxAg0qTLQ2xTF+iSn3/L3al0AFzD4nj1NTbLVwmM5Z4qC5tAr+rnl5IYOcW1D6jO0Wct\nE2K0WjFQTu0/Hxe+u2GCtHtoDik2yaznxtfKoRYBYlJkh5tkrfh7LVVE4xIYBlBURop/DYAywRgj\nDnhoHIrX0kCRx0ShAUT8OI/3ku59ch4SRMnjszBSXSGqWrkWp0HgajuAKmSzuA8S0JLug4PBoAZl\n+/fvx2AwUN0Ht7a2dmzeo9EIV1xxBZ761KeiLEu86EUvwmmnnYYrr7wSAHD55ZfjoosuwnXXXYdH\nPepRWFtbwzvf+c5o296OjfWM1e6Z6WAh+kt/jIyrAQGVMMXm5mZ9c1xbW6tvunth1locPnwYJ510\n0tx9vP/cNRj4rBMBK6BhqYDGDZCOE+iSCxK55tbAVKhswBYiljFYsl96yddJfFFgTLucm3Z4FnA8\nD7iSv2vOnAR/897usPNAFm/itRdgjJfxasPRwC/jrlVCDVCWAb4LonQbtEzOXJY567zrZ4VLl9ev\nWJXJ+CmalwZ+Yn2FQFqw/mjQisvRgBXQXBcOEEZCVr3qwH+b4sInk1BrUv6zWhLrndCtTBRcFrYF\nwKtjrE5pW254cjpyfoPhoGaiALSYKP7TlIt62fdw4Cv3jRjgCG0OAQ2w0pT8JMDQAJQ8zssygbl5\nXBe/VJzV53ejUE4oT4pcMFKyn9zpG1Wh44UiUlEEXAXVcQPz4RYKgP8/dgFUpRoBLVorWGtrgEUK\nhLRWkDFX1lpkWYbf/u3fxle+8hXccsstx/UG7YLZcXchjTHuY086cbXr/ts/WDin3CiOkZ24V/Y4\nM5k1nRSARqMRDh48uKegCti+K6AEVUaAKlIApDICOiRWQexU4fyHfCjprzwuQVWl8mcqMYtt/P46\nFQDn7rkxruo3dxLgvESZlzMF6hNb0PWxN/XCFYuOZDpdCWS7ci7FyuPy32nXk4O9srCqIEGorxB7\nEqyvzDcluW6sruZeF2OM/HxXbYXCJMVBbR4dqnxl3r62WuyXNgeZPLnL8pD/1xztMtu+D8VyKkmL\nS4WHy2IKWLzPLUUyPSSMofUt9lLq9qoUfNluq7JCaK4RL+bqf7JZbk3wfqQdD7FRoeMxVbG9BFVA\nxUgtLy9j//79OHDgAA4ePIh9+/YBqFgo2pgdj8f493//d3zjG9+o2aof/OAHePazn43HPOYxuPnm\nm3tQ1RusMyfs315b7wq4YFaWJTY2NmpVn/379+/1lDzT1IZids2T1gA0IMowgDM01UNsxNz8ate/\ngfNAC3d7IfEKniSYyr16oj3QPDQ177KB4krDXQOpeGAAWn9o3jch5mp5h7YxJHMwc3tNcS2weCun\nMVV1rFNQmr1yORktUz2lTmYxXB5Ek6Dm46LuQxoBEU9ogK3sirzNWtRjFzaYsFXNVzVdYYWub9gt\nsN1XdbxUmR81N1VeXSc+Fu9Dtm+5FRYOw6W032jIja+znRI/1nUsBOpjCoAx5UJtvi0himksFYE1\nKR4hXfYo5olsnFshgON/d2X9mJrfRuEz7oWyKQSAMU5N4UZhsDRNF1G75ilgaVya1v1Hi8vaLJu5\nOIQ3gLioA3fP48qAvN9Q/JTm2kcfmxaHpRln51LisDTwNA+W3mtAFTLa7MzzHPv27cPS0lKl5FoU\n+OpXv4oXv/jFyLIMZ5xxBr7xjW/gNa95DS677LKkBMS9nfjWuwLunvW/sAUx5xy2trZw3333YXl5\nGevr63s9Jc8oUeEsrBWBKlL046DKoHnwWjQPVQJVgM86EeCiL6wGmqRJdktbPHjuLozBovwn1Ifq\nzhc9ezEOqgUA/e2UaUxWymdU5hZlYKGrJgLWGBPlPLoYsTKzXh0tf0+sD1e6qLgBL2spssXaRdij\nGBAE2i6ErT7mSCIcmqvKRilz58fqnExZm43S3qvzUcctW69TYpvq+cRYxsA1G08Kv94cEvAynxSB\nJWKiZPMuJiqmtSHrhoRytHHKxJ1X+fXk72NfTT4XBx+AkcXOTY5DMVS8ycTqeax4v/z4RImdstBj\nqrLIvXTW1H+LylKFzDmHyWSCra0trK6uYmVlpRa7WFlZwU//9E/jn//5n/Ha174Wo9EIF1xwAa66\n6iqcfPLJOP/88/Ha174W1157LfI83+tT6W2PzJ7Af3ttPWO1IEb+0wcPHsRwOKyFK2ZliHbbUoHV\nNU9a82KPamBkmpwgMTdAYo8IbPFR+YM/xFrFLtnQNIsK2hROZbBmFIYLmuZOZAw6lcdiRgtK53Sm\nRWeR4nmlPLGBvKyAr8Iu8JxrReYzF07LDZWVQWaKykNqb9W8fVaHj6OVyXYaGAoxJ9Y6j1Wq2Y/C\nqr/N0LkRKJJtQvVj55Fi2vmUmW1tp8l6UvykSZqbxlLRce21HCP0HmiDK025EKh+S0vsByxZJC2R\nc4oboAYqtGMxmXSgAlepzNRW2ZY+p3q5bVgrKZEekguny8rZpRC444yRL4zhK7NuM1950LpU/rRL\nrLFcszBVsT2TRQZVW1tbsNZifX1dZaCyLMNrX/tajMdjfPCDH6xdBu+77z7ceuutuOWWW/CWt7wF\nT33qU4/19HtbEOsZq92zXrxiQYzU/7j953/+J0466aSFAVb33nsvDhw44OXj0EyCKs4yEaCiMyJ3\nFMPjrYyDdQYjJiShyalT/hGORXgMF/VfOP/hS/X5VdXcBwlY8Xq8vIsB847rh5u+Ih/xrGCL/6Y5\nwPJ+6oHf/XA0FAIU/DWrtzTwtoY4sOL1RstDD1jJpNccPEkAZq1rAQ7ZVwzA+TmP/DIjVq/UdqiI\nYBCwoLl0CUvMUp/nTBotD9sAQ3psksgE5c7ibqFLg9Z5alaWcSAlpftlXqd5TApJBOfVITbRiEYY\n7z0HVlJYgsAQBz+T0n+fWUB6T8qzli5+S8ZXuqP+xmUDgOpzER/LyECISbjpPHzAJEUnqF9yA9RS\nS5ANTBtYAdUx/pUdmbbin9afpgwox5Hu23UdVj9XjufWeG1DSX654EXouLxbhjwO5HOBbFEBFVCF\nCmxubmI4HGL//v3q2uB73/seLrvsMjzjGc/AS1/60oVZP5zAdtxdYGOM+9snbC8VyCLbM28t91S8\nomesFtjI9W5RbowproB/+aS1OscUgSqLKWOFJmcV4EusA/xB3IAqOh5bQJDVMsJAcEtAwygaW8Vz\nwYSAVXOsGUyLuVrZpsMtuSo55y8gNZOfz6y5h1LzWpEYRWc+q8xPBCwtFl9D7WPMVogxsdbCZgi2\n9XJkcdGD3LZAV9dceF8chBRZ2epLAiPZf0v9r+P6yLpdSYZbLFAH/VAqMVytOoly6175dB6x7wbg\nx0RxlknGRhFrlcJEhXRUcueDK8lEbZX6vULti7FLBIJGDGzFmCl+v9sSACq3puWCxwEf73PM5ksb\nUNrHPS71OKdYAl9eb8JIUB7jJCXYB2gDIt6PnzzYqPf5idXnFBIKoX0GevbwY3J8YLFBVZ7n2Nra\nwsrKCpaXl9V1wRe+8AX82q/9Gt74xjfivPPO24NZ9na82CK4zJ2o1gOrBTHtJrnTSXm3a7H5/CXF\nU4G5/Bk/dqp2CYTvBsgfqDyHFZUDfqwV/6/FWhlZR5mvp1pF58f60AGUeuq1hYr5rjbvI1FfwDO+\ncOwCWdwKzmx0LGaBaWxRwKXQ63c7iYCnp0KLe+5uxxmjbnBWBgOyi6xdVud1CSUDjoC5bCvHkJXF\n3OSAytVy2AHGukx16Qu5FapJgtvCD3qfaY/aLiAVinGSSXm99uReKVirmEkQJd9PU7M15TacI0ra\nZI5VR279uCgOrqr5GA9cxSyUby9XABRn0WLiGRxohfJEAT5Q4uCKA7B6PqqLow6WJtZAc6+eWNOq\nL4UtuMUAH9CAKEnecnDl9YdqvosKqiieKssyrK6uqgrBzjm8973vxTXXXIMPfehDOPXUU/dgpr0d\nT9YROtzbNqwHVgtkErgcL8CKgyqgAVWAHzvl0IAqUgOsy5yvCEjGdxQ5qKpV/qZlvC9pHHDViX7Z\nXKV1ufv5ddM/HzkW7ZDnDljuGEiVEp4TZFFenpQ2tGDOcoulAMjKs0pQoCsRcBdQi7EcnYmEo6px\nkbIAKCNwNYsbXJm3GadZ6lMsEM3VSxKsqf+VDsNQptmk8fW4Jg5smjnFQZPa//TzbIll8POavvYS\n4ZYWkxJYmX5kJDbRAkZuvs0Jbrn1ye0Qa6Up6x0tqhccPIUAkT9mNzMF6IBJs3nLnGvujTGgFVIG\n5J+qFuvEjc6Zx89yNz/ePgTM+NeVg6tcYbFCHrGh44sMqjY3N+Gci8ZT/eZv/iaKosANN9yAlZWV\nPZhpb8ebLc7K8sSzXhVwge14AFbvPWcNlvmwc/U/DqqARgmQQFXBHtaeq18giFnmp+JxVE3b6s+5\natdTu3zal74bQHVUmNNoxzezcQWuzn5Kh8mMWsJ56ZCxlUboqyYXxiGVvCR1uUAd6lMrpzKe60rG\nalVtu8s040p7fNEflAdPzAVGoITqS5AWUhOMzbVd17ZeN3me2HkV5VzqhF3jyvG7FAdVIYnAtLjL\nXsx9r65j20yT7HvDFxXUx53zMmXKfWuzEIyiqJOq2gdUjJFspyn5bYlrVTq9njxPLVeVZlRP3l8t\n9PxTqY8wCdTIMhv+jswiVBE6/swFBVVlWeLo0aMYDAZq0l8AuOeee/CMZzwDP/ETP4G3v/3tPajq\nLdl43rYT7U8zY8zTjDFfN8bcbox5TaDOm6bl/2iMOYMdf4cx5nvGmP835dr2jNUC26IBK8CP4Xnv\nOU2OKgem+CeAErkB8rrSz71mu9hYpTUYDpzKWhGo0gKkNRCk7caGgq5pA9pjrjSAZnzXn7ou0Ape\nTzUJrmYVhePtqW3XTLLCYVkwH9r3jpiumJgGuRwOh+F8VV3xN3ked/0r8jKSr6oM5qvSyrqk0kNM\nWZmF+tJZOa1+NSf9WpRF2++q67rJecvvvCYOATSuodIdj4OgVFnzzPrfWfkeCLvg0fFYLmnJIGk2\nsVVcIwEHOV7hms0YAkP89ypd+KSVzgdIsr4WEzqsx8N0vKZcY6Zo7nyus1gqiyX791gh+HFR/CML\n5Y7ijFTdfnqtuuKnAMyUVFljsEIuhNp4iwqogCaeat++fVheXlbrfP7zn8erX/1q/Omf/inOPffc\nYzzD3o53W6yV5e6aMWYI4AoA/wXAXQA+b4z5qHPua6zORQAe5Zx7tDHmbABvBfCEafE7AbwZwLtT\nxuuB1QLZ8eAKSMZBFeCLUvDYKnrvwEARmEsgO05CFwM0oAoQYMs1fQBxt5sm4JvN06BO7ktrIQ9U\naecdHiJoIelgAFgZpn+mmgpZqhiGtogL7eZkRQVgV5QL2srjw+StgwmDS4tBxC0u5lpI7aPgqrAY\nTdtLAMfLYu2847kGlBoGaLQ0bLEtob4IcLQSos5YX7N5E/rWdZXrGjomp6OBpBTj7bpYWclAaCBL\n1skju5RyHmRtQFGBIxKa4GBpI8HlT4pRlIlz0uayqYhk0Dn77oNtAMd/qxKk8TEmyrWgY54AhvVF\ngerYK7TvlZq7nxY/JV/z+XKz7JiDfx/WgFII7BW2PdaigqrUeKr3vOc9+MAHPoCPfOQjeNjDHrYH\nM+3teLcFWloeCzsLwDedc98BAGPM+wFcAuBrrM7TAbwLAJxztxljHmCMeYhz7h7n3M3GmEekDtYD\nqwW2RQRWzjm8ZwqqOFACGtYKaLsBUlwVl1yn47QA0B7WpTU1ApJ9chsAdf4qWtDU8VSB+jGb1/Uv\npRkt3vg4KQwX7eZq4Cq2XqXF6YogXjTXH3In7FpAS0lroL0D1gXAuhiwELiy075SAJTGmgUBTgTM\nFXnpiWt09VVYP7cSxQlRfcmUtRaZdsp+Tecj2SMZy9XO5VT1T8dkUlxp87gJElCRoEkDYPIYsUgb\nRfd3LbMGyx2/D8kaHS2MYKH0fucx/vtNNQl6anYugZmSLoGhHFMp/VCZBDZcmCLGdo3LZsPLi4sq\nTes7XAMtXi8SPyV/XhI8EbiqcxCyMu3rHYohW2RQ1RVPNZlM8JrXVF5Mn/jEJ3rXv97mtp1zDD8u\n7BQAd7D3dwI4O6HOKQDumXWwPsZqgW0RgdXfPOWHqtdAO7YKU7c/dsy5pi5nt+hBqO1S0g8+xFrx\ndqXzH6BkKvPUsR6a5cew0zFXMYZLM4on6YoH4QuOSZkWx2VdtdAaK2yB/DqG+qN1el66llqb/Kxi\nsWFZbqMS2oWM6eFqghEmpyisniQ4AjD4POQ4Wl+heWvzCtWdBfBofWjHytK2+m2xQDY9QW7omDwu\nj+lgJyww0NQxM/9eqvEEGG2dsyw3HviS5XRpC+VeNrFtt7aUEEj6PfO6hW23le6DvC037TdM5x17\ntITisqRZNNfF26iJpJCR8Vc0H36vCsVU8e+GY8e06i1g5hYXVKXGUz3zmc/EmWeeiSuvvLIHVb1t\ny5w7cf+00028LPLGNdcCvGesFsg0RbFFAlYcVAEN+0SAilz+6CHHN5kdmgcn3w0lwMV3STXWqpZf\nNy74VQ/FUdHDmMdOlbwN7WryMR0rV0zbQJ/VTWogrgPthIdcBUOkw8RWc+8an5rXLoIJa9OtMtwv\nfc4pLmJddSalw8rQ1GyUNMnIkFViJe0YsXpcFj8mWZtgn4obXNeiONRX6PgsfWjzoeuV2q/cCOCq\ne3U9JfaJPje+kE8FV6E6KXFYxK4QsNFYq5j7nnwfYqf4OdP8ZMwRvyZHC+P9buT3QrI9pDKoXR/p\n8hdjpqRJZoozTlTGARSVjcWYqcqAHkvGNrykheTSuVsfNy0zv1IAACAASURBVAKfNCzfgJOy6qr7\nHwdzaKfn4Pbfb1xMUJUST3XbbbfhN37jN/Bnf/ZnOOecc47xDHs7EW1xVpbbt6/d5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k9YzV7lkPrBbcUhmrt/4UA1WGP7yqJ1bMJVC+Vuexg+UhUKaCOaPfALbLggH+zrMG+rpM7hqn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\nfPHFlpsVa5cOulyuBjVaqfR0BtRjOdnziqE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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from mpl_toolkits.mplot3d import Axes3D\n", "\n", "fig = plt.figure(figsize=(16, 10))\n", "ax = fig.gca(projection='3d')\n", "surf = ax.plot_surface(grid[0], grid[1], density, rstride=1, cstride=1, cmap='Oranges_r',\n", " linewidth=0, antialiased=False)\n", "ax.set_zlim(0, 0.1)\n", "fig.colorbar(surf, shrink=0.5, aspect=5)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Можно загрузить картинку из файла.\n", "Это будет обычный numpy.array.\n", "Размерность картинки $280 x 280$.\n", "По последней координате цвета RGB и прозрачность." ] }, { "cell_type": "code", "execution_count": 58, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " (280, 280, 4)\n" ] }, { "data": { "image/png": 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IQnrvX1WHOjiGwZVsLx9QGJiofxj9igrF7DqyTRQhFvlRtJLX8Lnh87jgSWfd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\nCEn4/2EfMoTDqMd7AAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "picture = plt.imread('python.png')\n", "print(type(picture), picture.shape)\n", "\n", "plt.imshow(picture)\n", "plt.axis('off')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "У функций в matplotlib много параметров.\n", "Для того, чтобы посмотреть все параметры, можно воспользоваться справкой." ] }, { "cell_type": "code", "execution_count": 59, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [], "source": [ "# help(plt.plot)" ] } ], "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": "3.4.0" } }, "nbformat": 4, "nbformat_minor": 0 }