commit 05b1f6cdd5b339f01f6f546fe8cdf042842c83e7 Author: Lisa Schwetlick Date: Mon Aug 26 13:54:13 2024 +0200 Testing Class Material diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..921cafe --- /dev/null +++ b/.gitignore @@ -0,0 +1,70 @@ +# Byte-compiled / optimized / DLL files +__pycache__/ +*.py[cod] + +# C extensions +*.so + +# Distribution / packaging +.Python +env/ +build/ +develop-eggs/ +dist/ +downloads/ +eggs/ +.eggs/ +lib/ +lib64/ +parts/ +sdist/ +var/ +*.egg-info/ +.installed.cfg +*.egg +.pytest_cache + +# PyInstaller +# Usually these files are written by a python script from a template +# before PyInstaller builds the exe, so as to inject date/other infos into it. +*.manifest +*.spec + +# Installer logs +pip-log.txt +pip-delete-this-directory.txt + +# Unit test / coverage reports +htmlcov/ +.tox/ +.coverage +.coverage.* +.cache +nosetests.xml +coverage.xml +*,cover + +# Translations +*.mo +*.pot + +# Django stuff: +*.log + +# Sphinx documentation +docs/_build/ + +# PyBuilder +target/ + +#macos stuff +.DS_Store + +# PyCharm +.idea/ + +# Jupyter +.ipynb_checkpoints/ + +# general +_archive/ diff --git a/LICENSE.txt b/LICENSE.txt new file mode 100644 index 0000000..4b780a7 --- /dev/null +++ b/LICENSE.txt @@ -0,0 +1,6 @@ +The material in this repository is released under the +CC Attribution-Share Alike 4.0 International +license. + +Full license text available at +https://creativecommons.org/licenses/by-sa/4.0/ diff --git a/README.md b/README.md new file mode 100644 index 0000000..1c1775a --- /dev/null +++ b/README.md @@ -0,0 +1,2 @@ +# testing_debugging_profiling +Material for the class "Testing, debugging, profiling -- Python tools for building software" diff --git a/continuous_integration.pdf b/continuous_integration.pdf new file mode 100644 index 0000000..fc2dded Binary files /dev/null and b/continuous_integration.pdf differ diff --git a/continuous_integration.pptx b/continuous_integration.pptx new file mode 100644 index 0000000..20b66e4 Binary files /dev/null and b/continuous_integration.pptx differ diff --git a/debugging.pdf b/debugging.pdf new file mode 100644 index 0000000..1f34d05 Binary files /dev/null and b/debugging.pdf differ diff --git a/debugging.pptx b/debugging.pptx new file mode 100644 index 0000000..dbc0350 Binary files /dev/null and b/debugging.pptx differ diff --git a/extra_slides/code_organization_slides.pptx b/extra_slides/code_organization_slides.pptx new file mode 100644 index 0000000..86062eb Binary files /dev/null and b/extra_slides/code_organization_slides.pptx differ diff --git a/extra_slides/mocking.pptx b/extra_slides/mocking.pptx new file mode 100644 index 0000000..6cea8d0 Binary files /dev/null and b/extra_slides/mocking.pptx differ diff --git a/extra_slides/mocking/code.py b/extra_slides/mocking/code.py new file mode 100644 index 0000000..78f05dd --- /dev/null +++ b/extra_slides/mocking/code.py @@ -0,0 +1,30 @@ + +>>> from smtplib import SMTP +>>> mock_smtp = Mock(spec=SMTP) + +>>> isinstance(mock_smtp, SMTP) +True + +>>> mock_smtp. + mock_smtp.assert_any_call mock_smtp.attach_mock mock_smtp.call_args + mock_smtp.assert_called_once_with mock_smtp.auth mock_smtp.call_args_list + mock_smtp.assert_called_with mock_smtp.auth_cram_md5 mock_smtp.call_count > + mock_smtp.assert_has_calls mock_smtp.auth_login mock_smtp.called + mock_smtp.assert_not_called mock_smtp.auth_plain mock_smtp.close + +>>> mock_smtp.bogus +--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) + in () +----> 1 mock_smtp.bogus + +/Users/pberkes/miniconda3/envs/gnode/lib/python3.5/unittest/mock.py in __getattr__(self, name) + 576 elif self._mock_methods is not None: + 577 if name not in self._mock_methods or name in _all_magics: +--> 578 raise AttributeError("Mock object has no attribute %r" % name) + 579 elif _is_magic(name): + 580 raise AttributeError(name) + +AttributeError: Mock object has no attribute 'bogus' + + diff --git a/extra_slides/mocking/demo_Mock.py b/extra_slides/mocking/demo_Mock.py new file mode 100644 index 0000000..26b7a38 --- /dev/null +++ b/extra_slides/mocking/demo_Mock.py @@ -0,0 +1,64 @@ +##### Mock basic +m = Mock() +m.x = 3 +m.x +m.f(1,2,3) +m.whatever(3, key=2) +m +m.f +m.g + +##### special attributes and assert methods +mock=Mock() +mock.f(2,3) +mock.f('a') + +mock.f.called +mock.add.called +mock.f.called +mock.f.call_args +mock.f.call_count +mock.f.call_args_list +mock.f.assert_called_with('a') +mock.f.assert_called_once_with('a') +mock.f.assert_called_with(2, 3) +mock.f.assert_any_call(2, 3) +mock.f.assert_has_calls(['a', (2,3)]) + +#### return_value and side_effect +mock.g.return_value = 7 +mock.g(32) +mock.g('r') + +# useful to simulate file errors or server errors +mock.g.side_effect = Exception('Noooo') +mock.g(2) +mock.g.side_effect = lambda x: x.append(2) +a=[1] +mock.g(a) +a + +mock.g.side_effect = [1, 4, 5] +mock.g() +mock.g() +mock.g() +mock.g() + +##### +mock = Mock() +mock.f(3,4) +mock.g('a') +mock.f.a() +mock.method_calls + +result = m.h(32) +result(1) +m.mock_calls + +##### spec +from chaco.api import Plot +m2 = Mock(spec=Plot) +isinstance(m2, Plot) +m2.add +m2.add(12,'asdfasd') +m2.aaa diff --git a/extra_slides/mocking/report.py b/extra_slides/mocking/report.py new file mode 100644 index 0000000..c6d24d4 --- /dev/null +++ b/extra_slides/mocking/report.py @@ -0,0 +1,41 @@ +report_template = """ +Report +====== + +The experiment was a {judgment}! +Let's do this again, with a bigger budget. +""" + + +def send_report(result, smtp): + if result > 0.5: + judgment = 'big success' + else: + judgment = 'total failure' + report = report_template.format(judgment=judgment) + smtp.send_message( + report, + from_addr='pony@magicpony.com', + to_addrs=['ferenc@magicpony.com'], + ) + + +from unittest.mock import Mock + +def test_send_report_success(): + smtp = Mock() + + send_report(0.6, smtp) + assert smtp.send_message.call_count == 1 + pos_args, kw_args = smtp.send_message.call_args + message = pos_args[0] + assert 'success' in message + + smtp.reset_mock() + + send_report(0.4, smtp) + assert smtp.send_message.call_count == 1 + args, kwargs = smtp.send_message.call_args + message = args[0] + assert 'failure' in message + diff --git a/extra_slides/mocking/telescope/telescope_driver.py b/extra_slides/mocking/telescope/telescope_driver.py new file mode 100644 index 0000000..56dc2d9 --- /dev/null +++ b/extra_slides/mocking/telescope/telescope_driver.py @@ -0,0 +1,13 @@ + +def connect(address): + import time + time.sleep(5) + return '1' + +def get_angle(address): + return 0.0 + +def set_angle(address, angle): + if angle < 0 or angle > 1.40: + raise IOError('Telescope jammed -- please call technical support') + return True diff --git a/extra_slides/mocking/telescope/telescope_model.py b/extra_slides/mocking/telescope/telescope_model.py new file mode 100644 index 0000000..9de285b --- /dev/null +++ b/extra_slides/mocking/telescope/telescope_model.py @@ -0,0 +1,30 @@ +import telescope_driver + + +class TelescopeModel(object): + + # Minimum safe elevation angle (see handbook). + MIN_ANGLE = 0.0 + + # Maximum safe elevation angle (see handbook). + MAX_ANGLE = 80.0 + + def __init__(self, address): + self.address = address + # Connect to telescope + self.connection = telescope_driver.connect(address) + # Get initial state of telescope. + self.current_angle = telescope_driver.get_angle(self.connection) + + def set_elevation_angle(self, angle): + """ Set the elevation angle of the telescope (in rad). + + If the angle is outside the range allowed by the manufacturer, + raise a ValueError. + """ + + if angle < self.MIN_ANGLE or angle > self.MAX_ANGLE: + raise ValueError('Unsafe elevation angle: {}'.format(angle)) + + telescope_driver.set_angle(self.connection, angle) + self.current_angle = angle diff --git a/extra_slides/mocking/telescope/test_telescope_model.py b/extra_slides/mocking/telescope/test_telescope_model.py new file mode 100644 index 0000000..6dc4e36 --- /dev/null +++ b/extra_slides/mocking/telescope/test_telescope_model.py @@ -0,0 +1,12 @@ +import numpy as np +from py.test import raises + +from telescope_model import TelescopeModel + + +def test_unsafe_elevation_angle(): + telescope = TelescopeModel(address='10.2.1.1') + elevation_angle = np.pi / 2.0 + + with raises(ValueError): + telescope.set_elevation_angle(elevation_angle) diff --git a/extra_slides/mocking/telescope/test_telescope_model_with_mock.py b/extra_slides/mocking/telescope/test_telescope_model_with_mock.py new file mode 100644 index 0000000..f5f23d6 --- /dev/null +++ b/extra_slides/mocking/telescope/test_telescope_model_with_mock.py @@ -0,0 +1,29 @@ +from unittest import mock + +import numpy as np +from py.test import raises + +from telescope_model import TelescopeModel + + +def test_unsafe_elevation_angle(): + with mock.patch('telescope_model.telescope_driver'): + telescope = TelescopeModel(address='10.2.1.1') + elevation_angle = np.pi / 2.0 + with raises(ValueError): + telescope.set_elevation_angle(elevation_angle) + + +def test_model_initialization(): + connection_id = 'bogus_connection' + initial_angle = 1.23 + + with mock.patch('telescope_model.telescope_driver') as driver: + driver.connect.return_value = connection_id + driver.get_angle.return_value = initial_angle + + telescope = TelescopeModel(address='10.2.1.1') + assert telescope.connection == connection_id + assert driver.connect.call_count == 1 + assert telescope.current_angle == initial_angle + diff --git a/extra_slides/packaging.pptx b/extra_slides/packaging.pptx new file mode 100644 index 0000000..c47d1f8 Binary files /dev/null and b/extra_slides/packaging.pptx differ diff --git a/extra_slides/packaging/noiser_project_final/noiser/__init__.py b/extra_slides/packaging/noiser_project_final/noiser/__init__.py new file mode 100644 index 0000000..e69de29 diff --git a/extra_slides/packaging/noiser_project_final/noiser/images/baboon_kandinsky.png b/extra_slides/packaging/noiser_project_final/noiser/images/baboon_kandinsky.png new file mode 100644 index 0000000..52e7731 Binary files /dev/null and b/extra_slides/packaging/noiser_project_final/noiser/images/baboon_kandinsky.png differ diff --git a/extra_slides/packaging/noiser_project_final/noiser/main.py b/extra_slides/packaging/noiser_project_final/noiser/main.py new file mode 100644 index 0000000..3169b7a --- /dev/null +++ b/extra_slides/packaging/noiser_project_final/noiser/main.py @@ -0,0 +1,22 @@ +import os.path + +import matplotlib.pyplot as plt +from scipy.ndimage import imread +from pkg_resources import resource_filename + +from noiser.noise import white_noise +from noiser.utils import copy_image + + +def main(): + path = resource_filename('noiser', os.path.join('images', 'baboon_kandinsky.png')) + print(path) + img = imread(path) + noisy = copy_image(white_noise(img, 20)) + plt.imshow(noisy) + plt.draw() + plt.show() + + +if __name__ == '__main__': + main() diff --git a/extra_slides/packaging/noiser_project_final/noiser/noise.py b/extra_slides/packaging/noiser_project_final/noiser/noise.py new file mode 100644 index 0000000..70a7e86 --- /dev/null +++ b/extra_slides/packaging/noiser_project_final/noiser/noise.py @@ -0,0 +1,7 @@ +import numpy as np + + +def white_noise(image, std): + noise = np.random.normal(scale=std, size=image.shape).astype(image.dtype) + noisy = image + noise + return noisy diff --git a/extra_slides/packaging/noiser_project_final/noiser/setup.py b/extra_slides/packaging/noiser_project_final/noiser/setup.py new file mode 100644 index 0000000..b1eccfb --- /dev/null +++ b/extra_slides/packaging/noiser_project_final/noiser/setup.py @@ -0,0 +1,8 @@ +from setuptools import setup, find_packages + +setup( + name='Noiser', + version='1.0', + packages=find_packages(), +) + diff --git a/extra_slides/packaging/noiser_project_final/noiser/tests/__init__.py b/extra_slides/packaging/noiser_project_final/noiser/tests/__init__.py new file mode 100644 index 0000000..e69de29 diff --git a/extra_slides/packaging/noiser_project_final/noiser/tests/test_noise.py b/extra_slides/packaging/noiser_project_final/noiser/tests/test_noise.py new file mode 100644 index 0000000..cdf6683 --- /dev/null +++ b/extra_slides/packaging/noiser_project_final/noiser/tests/test_noise.py @@ -0,0 +1,24 @@ +import numpy as np +from numpy.testing import assert_allclose + +from noiser.noise import white_noise + + +def test_white_noise(): + n_images, height, width = 201, 101, 102 + dtype = np.float32 + + # Create ``n_images`` identical image. + base_image = np.random.rand(1, height, width, 3).astype(dtype) - 0.5 + images = np.repeat(base_image, n_images, axis=0) + + std = 0.13 + noisy = white_noise(images, std=std) + + # dtype and shape are preserved. + assert noisy.dtype == dtype + assert noisy.shape == images.shape + + # Mean and std of noisy image match expectations. + assert_allclose(images.mean(0), base_image[0], atol=1e-4) + assert np.isclose((noisy - images).std(), std, atol=1e-4) diff --git a/extra_slides/packaging/noiser_project_final/noiser/tests/test_utils.py b/extra_slides/packaging/noiser_project_final/noiser/tests/test_utils.py new file mode 100644 index 0000000..96d5048 --- /dev/null +++ b/extra_slides/packaging/noiser_project_final/noiser/tests/test_utils.py @@ -0,0 +1,14 @@ +import numpy as np +from numpy.testing import assert_array_equal + +from noiser.utils import copy_image + + +def test_copy_image(): + height, width = 101, 102 + dtype = np.float32 + + image = np.random.rand(height, width, 3).astype(dtype) + copy = copy_image(image) + assert_array_equal(copy, image) + diff --git a/extra_slides/packaging/noiser_project_final/noiser/utils.pyx b/extra_slides/packaging/noiser_project_final/noiser/utils.pyx new file mode 100644 index 0000000..6808478 --- /dev/null +++ b/extra_slides/packaging/noiser_project_final/noiser/utils.pyx @@ -0,0 +1,15 @@ +import numpy as np +cimport numpy as np + + +def copy_image(np.ndarray img): + cdef int h = img.shape[0] + cdef int w = img.shape[1] + cdef int c = img.shape[2] + cdef np.ndarray copy = np.empty([h, w, c], dtype=img.dtype) + + for i in range(h): + for j in range(w): + for k in range(c): + copy[i, j, k] = img[i, j, k] + return copy diff --git a/extra_slides/packaging/noiser_project_final/setup.py b/extra_slides/packaging/noiser_project_final/setup.py new file mode 100644 index 0000000..287f0af --- /dev/null +++ b/extra_slides/packaging/noiser_project_final/setup.py @@ -0,0 +1,29 @@ +from Cython.Build import cythonize +import numpy +from setuptools import setup, find_packages +from setuptools.extension import Extension + + +extensions = [ + Extension( + 'noiser.utils', + ["noiser/utils.pyx"], + include_dirs=[numpy.get_include()], + ) +] + + +setup( + name='Noiser', + version='1.0', + packages=find_packages(), + ext_modules=cythonize(extensions), + entry_points={ + 'console_scripts': [ + 'baboon=noiser.main:main', + ] + }, + package_data={ + 'noiser': ['images/*.png'], + } +) diff --git a/extra_slides/profiling/residuals.py b/extra_slides/profiling/residuals.py new file mode 100644 index 0000000..610f133 --- /dev/null +++ b/extra_slides/profiling/residuals.py @@ -0,0 +1,31 @@ +import numpy as np +import theano +from theano import tensor as T + + +SLOPE = 3.1 +INTERCEPT = -1.2 + + +def residual_stats_theano(x, y): + expected = SLOPE * x + INTERCEPT + residuals = y - expected + return residuals.mean(), residuals.std() + + +x_var = T.vector() +y_var = T.vector() + +residual_stats = theano.function( + inputs=[x_var, y_var], + outputs=residual_stats_theano(x_var, y_var), + allow_input_downcast=True, +) + + +if __name__ == '__main__': + x = np.linspace(-10, 10, 1000) + y = SLOPE * x + INTERCEPT + y += np.random.normal(loc=0.1, scale=0.5, size=x.shape) + mn, std = residual_stats(x, y) + print('Residual mean=', mn, ', std=', std) diff --git a/extra_slides/profiling/residuals_profile.py b/extra_slides/profiling/residuals_profile.py new file mode 100644 index 0000000..f525f01 --- /dev/null +++ b/extra_slides/profiling/residuals_profile.py @@ -0,0 +1,35 @@ +import numpy as np +import theano +from theano import tensor as T + +theano.config.profile_memory = True +theano.config.profile = True + + +SLOPE = 3.1 +INTERCEPT = -1.2 + + +def residual_stats_theano(x, y): + expected = SLOPE * x + INTERCEPT + residuals = y - expected + return residuals.mean(), residuals.std() + + +x_var = T.vector() +y_var = T.vector() + +residual_stats = theano.function( + inputs=[x_var, y_var], + outputs=residual_stats_theano(x_var, y_var), + allow_input_downcast=True, + profile=True, +) + + +if __name__ == '__main__': + x = np.linspace(-10, 10, 1000) + y = SLOPE * x + INTERCEPT + y += np.random.normal(loc=0.1, scale=0.5, size=x.shape) + mn, std = residual_stats(x, y) + print('Residual mean=', mn, ', std=', std) diff --git a/hands_on/bug_hunt/datastore/README b/hands_on/bug_hunt/datastore/README new file mode 100644 index 0000000..e30ce2c --- /dev/null +++ b/hands_on/bug_hunt/datastore/README @@ -0,0 +1 @@ +This is the directory used as a datastore by `file_datastore.py`. diff --git a/hands_on/bug_hunt/file_datastore.py b/hands_on/bug_hunt/file_datastore.py new file mode 100644 index 0000000..a9e9a61 --- /dev/null +++ b/hands_on/bug_hunt/file_datastore.py @@ -0,0 +1,113 @@ +import os + + +class FileDatastore: + """Datastore based on a regular file system. + + Parameters + ---------- + base_path: str + Filesystem path at which the data store is based. + """ + + def __init__(self, base_path): + if not os.path.exists(base_path): + raise FileNotFoundError(f'Base path {base_path} does not exist') + if not os.path.isdir(base_path): + raise NotADirectoryError(f'Base path {base_path} exists but is not a directory') + + self.base_path = base_path + + def open(self, path, mode): + """ Open a file-like object + + Parameters + ---------- + path: str + Path relative to the root of the data store. + mode: str + Specifies the mode in which the file is opened. + + Returns + ------- + IO[Any] + An open file-like object. + """ + path = os.path.join(self.base_path, path) + return open(path, mode) + + def read(self, path): + """ Read a sequence of bytes from the data store. + + Parameters + ---------- + path: str + Path relative to the root of the data store. + + Returns + ------- + bytes + The sequence of bytes read from `path`. + """ + with self.open(path, 'rb') as f: + data = f.read() + return data + + def write(self, path, data) -> None: + """ Write a sequence of bytes to the data store. + + `path` contains the path relative to the root of the data store, including the name + of the file to be created. If a file already exists at `path`, it is overwritten. + + Intermediate directories that do not exist will be created. + + Parameters + ---------- + path: str + Path relative to the root of the data store. + data: bytes + Sequence of bytes to write at `path`. + """ + path = os.path.join(self.base_path, path) + self.makedirs(os.path.dirname(path)) + with self.open(path, 'wb') as f: + f.write(data) + + def exists(self, path): + """ Returns True if the file exists. + + Parameters + ---------- + path: str + Path relative to the root of the data store. + + Returns + ------- + bool + True if the file exists, false otherwise + """ + complete_path = os.path.join(self.base_path, path) + return os.path.exists(complete_path) + + def makedirs(self, path): + """ Creates the specified directory if needed. + + If the directories already exist, the method does not do anything. + + Parameters + ---------- + path: str + Path relative to the root of the data store. + """ + complete_path = os.path.join(self.base_path, path) + os.makedirs(complete_path, exist_ok=True) + + +if __name__ == '__main__': + data = b'A test! 012' + datastore = FileDatastore(base_path='./datastore') + datastore.write('a/mydata.bin', data) + + # This should pass! + # The code works correctly if `base_path` is an absolute path :-( + assert os.path.exists('./datastore/a/mydata.bin') diff --git a/hands_on/debugger/analyze_sums_and_differences.ipynb b/hands_on/debugger/analyze_sums_and_differences.ipynb new file mode 100644 index 0000000..367523f --- /dev/null +++ b/hands_on/debugger/analyze_sums_and_differences.ipynb @@ -0,0 +1,65 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "id": "30f3f04f", + "metadata": {}, + "outputs": [], + "source": [ + "from debugger_example import sum_over_difference" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3632cacb", + "metadata": {}, + "outputs": [], + "source": [ + "result = sum_over_difference(7, 5)\n", + "print(result)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "02577028", + "metadata": {}, + "outputs": [], + "source": [ + "result = sum_over_difference(12, 12)\n", + "print(result)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "58fc58c0", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "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": "3.11.3" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/hands_on/debugger/debugger_example.py b/hands_on/debugger/debugger_example.py new file mode 100755 index 0000000..74c0743 --- /dev/null +++ b/hands_on/debugger/debugger_example.py @@ -0,0 +1,23 @@ +def add(arg1, arg2): + return arg1 + arg2 + + +def sub(arg1, arg2): + return arg1 - arg2 + + +def div(arg1, arg2): + return arg1 / arg2 + + +def sum_over_difference(arg1, arg2): + """Compute sum of arguments over difference of arguments.""" + arg_sum = add(arg1, arg2) + arg_diff = sub(arg1, arg2) + sum_over_diff = div(arg_sum, arg_diff) + return sum_over_diff + + +if __name__ == '__main__': + result = sum_over_difference(7, 5) + print(result) diff --git a/hands_on/factorial/factorial.py b/hands_on/factorial/factorial.py new file mode 100644 index 0000000..9d8617c --- /dev/null +++ b/hands_on/factorial/factorial.py @@ -0,0 +1,33 @@ +""" Compute the factorial of a set of numbers stored in a file. """ + +def factorial(n): + if n == 0: + return 1 + else: + return factorial(n-1) * n + + +def read_data(filename): + numbers = [] + with open(filename, 'r') as f: + for line in f: + number = int(line) + numbers.append(number) + return numbers + + +def compute_factorials_for_list(numbers): + factorials = [] + for number in numbers: + result = factorial(number) + factorials.append(result) + return factorials + + +def main(): + numbers = read_data('numbers.txt') + factorials = compute_factorials_for_list(numbers) + + +if __name__ == '__main__': + main() diff --git a/hands_on/factorial/numbers.txt b/hands_on/factorial/numbers.txt new file mode 100644 index 0000000..8354c09 --- /dev/null +++ b/hands_on/factorial/numbers.txt @@ -0,0 +1,100000 @@ +40 +148 +275 +285 +89 +64 +123 +189 +72 +152 +109 +269 +89 +51 +122 +187 +186 +291 +12 +232 +133 +196 +32 +50 +260 +145 +121 +217 +268 +217 +259 +262 +277 +32 +78 +177 +132 +222 +94 +26 +150 +29 +171 +92 +249 +243 +258 +233 +188 +220 +74 +270 +271 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""" + +from factorial import factorial + + +def test_factorial(): + factorial_cases = [(1, 1), + (0, 1), + (5, 2*3*4*5), + (30, 265252859812191058636308480000000)] + + for n, fact_n in factorial_cases: + assert factorial(n) == fact_n diff --git a/hands_on/first/first.py b/hands_on/first/first.py new file mode 100644 index 0000000..abafde8 --- /dev/null +++ b/hands_on/first/first.py @@ -0,0 +1,8 @@ +def times_3(x): + """ Multiply x by 3. + + Parameters + ---------- + x : The item to multiply by 3. + """ + return x * 3 diff --git a/hands_on/first/test_first.py b/hands_on/first/test_first.py new file mode 100644 index 0000000..64ea1a8 --- /dev/null +++ b/hands_on/first/test_first.py @@ -0,0 +1,19 @@ +from first import times_3 + + +def test_times_3_integer(): + value = 7 + expected = 21 + + result = times_3(value) + + assert result == expected + + +def test_times_3_string(): + value = 'wow' + expected = 'wowwowwow' + + result = times_3(value) + + assert result == expected diff --git a/hands_on/first_teacher/first.py b/hands_on/first_teacher/first.py new file mode 100644 index 0000000..abafde8 --- /dev/null +++ b/hands_on/first_teacher/first.py @@ -0,0 +1,8 @@ +def times_3(x): + """ Multiply x by 3. + + Parameters + ---------- + x : The item to multiply by 3. + """ + return x * 3 diff --git a/hands_on/local_maxima/local_maxima.py b/hands_on/local_maxima/local_maxima.py new file mode 100644 index 0000000..db89ba3 --- /dev/null +++ b/hands_on/local_maxima/local_maxima.py @@ -0,0 +1,10 @@ +def find_maxima(x): + """Find local maxima of x. + + Input arguments: + x -- 1D list of real numbers + + Output: + idx -- list of indices of the local maxima in x + """ + return [] diff --git a/hands_on/local_maxima_part2/local_maxima.py b/hands_on/local_maxima_part2/local_maxima.py new file mode 100644 index 0000000..db89ba3 --- /dev/null +++ b/hands_on/local_maxima_part2/local_maxima.py @@ -0,0 +1,10 @@ +def find_maxima(x): + """Find local maxima of x. + + Input arguments: + x -- 1D list of real numbers + + Output: + idx -- list of indices of the local maxima in x + """ + return [] diff --git a/hands_on/local_maxima_part2/test_local_maxima.py b/hands_on/local_maxima_part2/test_local_maxima.py new file mode 100644 index 0000000..316442d --- /dev/null +++ b/hands_on/local_maxima_part2/test_local_maxima.py @@ -0,0 +1,30 @@ +from local_maxima import find_maxima + + +def test_find_maxima(): + values = [1, 3, -2, 0, 2, 1] + expected = [1, 4] + maxima = find_maxima(values) + assert maxima == expected + + +def test_find_maxima_edges(): + values = [4, 2, 1, 3, 1, 5] + expected = [0, 3, 5] + maxima = find_maxima(values) + assert maxima == expected + + +def test_find_maxima_empty(): + values = [] + expected = [] + maxima = find_maxima(values) + assert maxima == expected + + +def test_find_maxima_plateau(): + raise Exception('not yet implemented') + + +def test_find_maxima_not_a_plateau(): + raise Exception('not yet implemented') diff --git a/hands_on/local_maxima_part3_debug/local_maxima.py b/hands_on/local_maxima_part3_debug/local_maxima.py new file mode 100644 index 0000000..82727a6 --- /dev/null +++ b/hands_on/local_maxima_part3_debug/local_maxima.py @@ -0,0 +1,49 @@ +def find_maxima(x): + """Find local maxima of x. + + Input arguments: + x -- 1D list of real numbers + + Output: + idx -- list of indices of the local maxima in x + """ + + maxima = [] + + len_x = len(x) + if len_x == 0: + return maxima + + maxima = check_first_element(x, maxima) + maxima = check_last_element(x, maxima) + + # Check numbers in between + i = 1 + while i < len_x - 1: + if x[i] > x[i - 1]: + # We have found a potential maximum or start of a plateau + plateau_start = i + while i < len_x - 1 and x[i] == x[i + 1]: + i += 1 + plateau_end = i + if x[plateau_end] > x[plateau_end + 1]: + maxima.append(plateau_start) + i += 1 + return maxima + + +def check_first_element(x, maxima): + if x[0] > x[1]: + maxima.append(0) + return maxima + + +def check_last_element(x, maxima): + if x[-1] > x[-2]: + maxima.append(len(x) - 1) + return maxima + + +if __name__ == "__main__": + result = find_maxima([1, 2, 2, 1]) + print(result) diff --git a/hands_on/local_maxima_part3_debug/test_local_maxima.py b/hands_on/local_maxima_part3_debug/test_local_maxima.py new file mode 100644 index 0000000..008d9db --- /dev/null +++ b/hands_on/local_maxima_part3_debug/test_local_maxima.py @@ -0,0 +1,107 @@ +import numpy as np +import pytest + +from local_maxima import find_maxima + + +def test_find_maxima(): + values = [1, 3, -2, 0, 2, 1] + expected = [1, 4] + maxima = find_maxima(values) + assert maxima == expected + + +def test_find_maxima_edges(): + values = [4, 2, 1, 0, 1, 5] + expected = [0, 5] + maxima = find_maxima(values) + assert maxima == expected + + +def test_find_maxima_empty(): + values = [] + expected = [] + maxima = find_maxima(values) + assert maxima == expected + + +def test_find_maxima_plateau(): + values = [1, 2, 2, 1] + expected = [1] + maxima = find_maxima(values) + assert maxima == expected + + +def test_find_maxima_not_a_plateau(): + values = [1, 2, 2, 3, 1] + expected = [3] + maxima = find_maxima(values) + assert maxima == expected + + +# the tests below here fail, can you get them to pass? + + +def test_find_maxima_correct_order(): + # TASK: get this test to pass + values = [2, 1, 5, 1, 9] + expected = [0, 2, 4] + maxima = find_maxima(values) + assert maxima == expected + + +def test_find_maxima_one_value(): + # TASK: get this test to pass + values = [1] + expected = [0] + maxima = find_maxima(values) + assert maxima == expected + + +def test_find_maxima_long_plateau(): + # TASK: Change the implementation for when there is a plateau + # for uneven plateau length, return the middle index, e.g. [1, 2, *2*, 2, 1] --> [2] + # for even plateau length, return the index left of the middle e.g. [1, 2, *2*, 2, 2, 1] --> [2] + values = [1, 2, 2, 2, 2, 2, 1, 8, 0] + expected = [3, 7] + maxima = find_maxima(values) + assert maxima == expected + + +def test_find_maxima_plateau_at_end(): + # TASK: make sure plateaus at the end are handled properly (see test above) + values = [1, 2, 2] + expected = [1] + maxima = find_maxima(values) + assert maxima == expected + + +def test_find_maxima_plateau_at_start(): + # TASK: make sure plateaus at the start are handled properly (see test above) + values = [1, 1, 0, 0] + expected = [0] + maxima = find_maxima(values) + assert maxima == expected + + +def test_find_maxima_all_same_values(): + # TASK: implement a check for lists where there is no local maximum + values = [1, 1] + expected = [0] + maxima = find_maxima(values) + assert maxima == expected + + +def test_find_maxima_letters(): + # stings can be evaluated with > and <, who knew! + # Find an easy solution so that both "t"s are recognised as local maxima + values = ["T", "e", "s", "t", "s", "!"] + expected = [0, 3] + maxima = find_maxima(values) + assert maxima == expected + + +def test_find_maxima_new_inputs_to_make_current_function_fail(): + # should you actually be done with all tests, then you can think of other cases where the current function fails + # and write tests for them and fix them + assert False diff --git a/hands_on/logistic_fun/readme.md b/hands_on/logistic_fun/readme.md new file mode 100644 index 0000000..a049497 --- /dev/null +++ b/hands_on/logistic_fun/readme.md @@ -0,0 +1 @@ +This exercise is in a separate repo! diff --git a/hands_on/numpy_equality/test_numpy_equality.py b/hands_on/numpy_equality/test_numpy_equality.py new file mode 100644 index 0000000..a1a52e7 --- /dev/null +++ b/hands_on/numpy_equality/test_numpy_equality.py @@ -0,0 +1,22 @@ +import numpy as np + + +def test_equality(): + x = np.array([1, 1]) + y = np.array([2, 2]) + z = np.array([3, 3]) + assert x + y == z + + +def test_equality_with_nan(): + x = np.array([1, np.nan]) + y = np.array([2, np.nan]) + z = np.array([3, np.nan]) + assert x + y == z + + +def test_allclose_with_nan(): + x = np.array([1.1, np.nan]) + y = np.array([2.2, np.nan]) + z = np.array([3.3, np.nan]) + assert x + y == z diff --git a/hands_on_solutions/first/first.py b/hands_on_solutions/first/first.py new file mode 100644 index 0000000..abafde8 --- /dev/null +++ b/hands_on_solutions/first/first.py @@ -0,0 +1,8 @@ +def times_3(x): + """ Multiply x by 3. + + Parameters + ---------- + x : The item to multiply by 3. + """ + return x * 3 diff --git a/hands_on_solutions/first/test_first.py b/hands_on_solutions/first/test_first.py new file mode 100644 index 0000000..b708f12 --- /dev/null +++ b/hands_on_solutions/first/test_first.py @@ -0,0 +1,28 @@ +from first import times_3 + + +def test_times_3_integer(): + value = 7 + expected = 21 + + result = times_3(value) + + assert result == expected + + +def test_times_3_string(): + value = 'wow' + expected = 'wowwowwow' + + result = times_3(value) + + assert result == expected + + +def test_times_3_list(): + value = [1] + expected = [1, 1, 1] + + result = times_3(value) + + assert result == expected diff --git a/hands_on_solutions/local_maxima/local_maxima.py b/hands_on_solutions/local_maxima/local_maxima.py new file mode 100644 index 0000000..83a49ac --- /dev/null +++ b/hands_on_solutions/local_maxima/local_maxima.py @@ -0,0 +1,44 @@ +def find_maxima(x): + """Find local maxima of x. + + Example: + >>> x = [1, 3, -2, 0, 2, 1] + >>> find_maxima(x) + [1, 4] + + If in a local maximum several elements have the same value, + return the left-most index. + Example: + >>> x = [1, 2, 2, 1] + >>> find_maxima(x) + [1] + + Input arguments: + x -- 1D list of real numbers + + Output: + idx -- list of indices of the local maxima in x + """ + + idx = [] + up = False + down = False + for i in range(len(x)): + if i == 0 or x[i-1] < x[i]: + up = True + up_idx = i + elif x[i-1] > x[i]: + up = False + + # if x[i-1] == x[i], no change + + if i+1 == len(x) or x[i+1] < x[i]: + down = True + elif x[i+1] > x[i]: + down = False + + if up and down: + idx.append(up_idx) + + return idx + diff --git a/hands_on_solutions/local_maxima/test_local_maxima.py b/hands_on_solutions/local_maxima/test_local_maxima.py new file mode 100644 index 0000000..d6561f5 --- /dev/null +++ b/hands_on_solutions/local_maxima/test_local_maxima.py @@ -0,0 +1,36 @@ +from local_maxima import find_maxima + + +def test_find_maxima(): + values = [1, 3, -2, 0, 2, 1] + expected = [1, 4] + maxima = find_maxima(values) + assert maxima == expected + + +def test_find_maxima_edges(): + values = [4, 2, 1, 3, 1, 5] + expected = [0, 3, 5] + maxima = find_maxima(values) + assert maxima == expected + + +def test_find_maxima_empty(): + values = [] + expected = [] + maxima = find_maxima(values) + assert maxima == expected + + +def test_find_maxima_plateau(): + values = [1, 2, 2, 1] + expected = [1] + maxima = find_maxima(values) + assert maxima == expected + + +def test_find_maxima_not_a_plateau(): + values = [1, 2, 2, 3, 1] + expected = [3] + maxima = find_maxima(values) + assert maxima == expected diff --git a/hands_on_solutions/local_maxima_part3_debug/local_maxima_solution.py b/hands_on_solutions/local_maxima_part3_debug/local_maxima_solution.py new file mode 100644 index 0000000..806067b --- /dev/null +++ b/hands_on_solutions/local_maxima_part3_debug/local_maxima_solution.py @@ -0,0 +1,67 @@ +import math + +import numpy as np + + +def find_maxima(x): + """Find local maxima of x. + + Input arguments: + x -- 1D list of real numbers + + Output: + idx -- list of indices of the local maxima in x + """ + maxima = [] + len_x = len(x) + if len_x == 0: + return maxima + elif len_x == 1: + return [0] + + # additional checks + if np.all([isinstance(item, str) for item in x]): + x = [item.lower() for item in x] + if np.all([item == x[0] for item in x]): + return [0] + + maxima = check_first_element(x, maxima) + # Check numbers in between + i = 1 + while i < len_x - 1: + if x[i] >= x[i - 1]: + # We have found a potential maximum or start of a plateau + # breakpoint() + if i == 1 and x[i] == x[i - 1]: + plateau_start = i - 1 + else: + plateau_start = i + while i < len_x - 1 and x[i] == x[i + 1]: + i += 1 + plateau_end = i + if plateau_end == len_x - 1: + maxima.append((plateau_end + plateau_start) // 2) + elif x[plateau_end] > x[plateau_end + 1]: + maxima.append((plateau_end + plateau_start) // 2) + i += 1 + maxima = check_last_element(x, maxima) + + return maxima + + +def check_first_element(x, maxima): + if x[0] > x[1]: + maxima.append(0) + return maxima + + +def check_last_element(x, maxima): + if x[-1] > x[-2]: + maxima.append(len(x) - 1) + return maxima + + +if __name__ == "__main__": + # result = find_maxima([1, 3, -2, 0, 2, 1]) + result = find_maxima([1, 2, 2, 1]) + print(result) diff --git a/hands_on_solutions/local_maxima_part3_debug/test_local_maxima_solution.py b/hands_on_solutions/local_maxima_part3_debug/test_local_maxima_solution.py new file mode 100644 index 0000000..4be4adb --- /dev/null +++ b/hands_on_solutions/local_maxima_part3_debug/test_local_maxima_solution.py @@ -0,0 +1,97 @@ +import numpy as np +import pytest + +from local_maxima_solution import find_maxima + + +def test_find_maxima(): + values = [1, 3, -2, 0, 2, 1] + expected = [1, 4] + maxima = find_maxima(values) + assert maxima == expected + + +def test_find_maxima_edges(): + values = [4, 2, 1, 0, 1, 5] + expected = [0, 5] + maxima = find_maxima(values) + assert maxima == expected + + +def test_find_maxima_empty(): + values = [] + expected = [] + maxima = find_maxima(values) + assert maxima == expected + + +def test_find_maxima_plateau(): + values = [1, 2, 2, 1] + expected = [1] + maxima = find_maxima(values) + assert maxima == expected + + +def test_find_maxima_not_a_plateau(): + values = [1, 2, 2, 3, 1] + expected = [3] + maxima = find_maxima(values) + assert maxima == expected + + +# the tests below here fail, can you get them to pass? + + +def test_find_maxima_correct_order(): + values = [2, 1, 5, 1, 9] + expected = [0, 2, 4] + maxima = find_maxima(values) + assert maxima == expected + + +def test_find_maxima_one_value(): + values = [1] + expected = [0] + maxima = find_maxima(values) + assert maxima == expected + + +def test_find_maxima_long_plateau(): + values = [1, 2, 2, 2, 2, 2, 1, 8, 0] + expected = [3, 7] + maxima = find_maxima(values) + assert maxima == expected + + +def test_find_maxima_plateau_at_end(): + values = [1, 2, 2] + expected = [1] + maxima = find_maxima(values) + assert maxima == expected + + +def test_find_maxima_plateau_at_start(): + values = [1, 1, 0, 0] + expected = [0] + maxima = find_maxima(values) + assert maxima == expected + + +def test_find_maxima_all_same_values(): + values = [1, 1] + expected = [0] + maxima = find_maxima(values) + assert maxima == expected + + +def test_find_maxima_letters(): + values = ["T", "e", "s", "t", "s", "!"] + expected = [0, 3] + maxima = find_maxima(values) + assert maxima == expected + + +def test_find_maxima_new_inputs_to_make_current_function_fail(): + # should you actually be done with all tests, then you can think of other cases where the current function fails + # and write tests for them and fix them + assert True diff --git a/hands_on_solutions/logistic_fun/bifurcation.png b/hands_on_solutions/logistic_fun/bifurcation.png new file mode 100644 index 0000000..3a45d32 Binary files /dev/null and b/hands_on_solutions/logistic_fun/bifurcation.png differ diff --git a/hands_on_solutions/logistic_fun/conftest.py b/hands_on_solutions/logistic_fun/conftest.py new file mode 100644 index 0000000..7429839 --- /dev/null +++ b/hands_on_solutions/logistic_fun/conftest.py @@ -0,0 +1,28 @@ +import numpy as np +import pytest + + +# add a commandline option to pytest +def pytest_addoption(parser): + """Add random seed option to py.test. + """ + parser.addoption('--seed', dest='seed', type=int, action='store', + help='set random seed') + + +# configure pytest to automatically set the rnd seed if not passed on CLI +def pytest_configure(config): + seed = config.getvalue("seed") + # if seed was not set by the user, we set one now + if seed is None or seed == ('NO', 'DEFAULT'): + config.option.seed = int(np.random.randint(2**31-1)) + + +def pytest_report_header(config): + return f'Using random seed: {config.option.seed}' + + +@pytest.fixture +def random_state(request): + random_state = np.random.RandomState(request.config.option.seed) + return random_state diff --git a/hands_on_solutions/logistic_fun/conftest2.py b/hands_on_solutions/logistic_fun/conftest2.py new file mode 100644 index 0000000..f68b341 --- /dev/null +++ b/hands_on_solutions/logistic_fun/conftest2.py @@ -0,0 +1,10 @@ +import numpy as np +import pytest + +SEED = 42 + +@pytest.fixture +def random_state(): + print(f'Seed: {SEED}') + random_state = np.random.RandomState(SEED) + return random_state diff --git a/hands_on_solutions/logistic_fun/logistic.py b/hands_on_solutions/logistic_fun/logistic.py new file mode 100644 index 0000000..0853ef4 --- /dev/null +++ b/hands_on_solutions/logistic_fun/logistic.py @@ -0,0 +1,25 @@ +import numpy as np + + +def f(x, r): + """ + takes r and x as input and returns r*x*(1-x) + """ + return r * x * (1 - x) + + +def iterate_f(it, xi, r): + """ + takes a number of iterations `it`, a starting value, + and a parameter value for r. It should execute f repeatedly (it times), + each time using the last result of f as the new input to f. Append each + iteration's result to a list l. Finally, convert the list into a numpy + array and return it. + """ + x = xi + xs = [] + for _ in range(it): + x = f(x, r) + xs.append(x) + + return np.array(xs) diff --git a/hands_on_solutions/logistic_fun/plot_logfun.py b/hands_on_solutions/logistic_fun/plot_logfun.py new file mode 100644 index 0000000..a3faf07 --- /dev/null +++ b/hands_on_solutions/logistic_fun/plot_logfun.py @@ -0,0 +1,70 @@ +"""Usage: +``` +plot_trajectory(100, 3.6, 0.1) +plot_bifurcation(2.5, 4.2, 0.001) +``` +""" +import numpy as np +from matplotlib import pyplot as plt + +from logistic import iterate_f + + +def plot_trajectory(n, r, x0, fname="single_trajectory.png"): + """ + Saves a plot of a single trajectory of the logistic function + + inputs + n: int (number of iterations) + r: float (r value for the logistic function) + x0: float (between 0 and 1, starting point for the iteration) + fname: str (filename to which to save the image) + + returns + fig, ax (matplotlib objects) + """ + l = iterate_f(n, x0, r) + fig, ax = plt.subplots(figsize=(10, 5)) + ax.plot(list(range(n)), l) + fig.suptitle('Logistic Function') + + fig.savefig(fname) + return fig, ax + + +def plot_bifurcation(start, end, step, fname="bifurcation.png", it=100000, + last=300): + """ + Saves a plot of the bifurcation diagram of the logistic function. The + `start`, `end`, and `step` parameters define for which r values to + calculate the logistic function. If you space them too closely, it might + take a very long time, if you dont plot enough, your bifurcation diagram + won't be informative. Choose wisely! + + inputs + start, end, step: float (which r values to calculate the logistic + function for) + fname: str (filename to which to save the image) + it: int (how many iterations to run for each r value) + last: int (how many of the last iterates to plot) + + + returns + fig, ax (matplotlib objects) + """ + r_range = np.arange(start, end, step) + x = [] + y = [] + + for r in r_range: + l = iterate_f(it, 0.1, r) + ll = l[len(l) - last::].copy() + lll = np.unique(ll) + y.extend(lll) + x.extend(np.ones(len(lll)) * r) + + fig, ax = plt.subplots(figsize=(20, 10)) + ax.scatter(x, y, s=0.1, color='k') + ax.set_xlabel("r") + fig.savefig(fname) + return fig, ax diff --git a/hands_on_solutions/logistic_fun/plot_script.py b/hands_on_solutions/logistic_fun/plot_script.py new file mode 100644 index 0000000..64edfb8 --- /dev/null +++ b/hands_on_solutions/logistic_fun/plot_script.py @@ -0,0 +1,3 @@ +from plot_logfun import plot_trajectory + +plot_trajectory(100, 3.4, 0.1) \ No newline at end of file diff --git a/hands_on_solutions/logistic_fun/readme.md b/hands_on_solutions/logistic_fun/readme.md new file mode 100644 index 0000000..5b68366 --- /dev/null +++ b/hands_on_solutions/logistic_fun/readme.md @@ -0,0 +1,81 @@ +# Testing Project for ASPP 2023 Mexico + +## Exercise 1 -- @parametrize and the logistic map + +Make a file `logistic.py` and `test_logistic.py` in the same folder as this +readme and the `plot_logfun.py` file. Implement the code for the logistic map +in the `logistic.py` file: + +a) Implement the logistic map f(𝑥)=𝑟∗𝑥∗(1−𝑥) . Use `@parametrize` +to test the function for the following cases: +``` + x=0.1, r=2.2 => f(x, r)=0.198 + x=0.2, r=3.4 => f(x, r)=0.544 + x=0.75, r=1.7 => f(x, r)=0.31875 +``` + +b) Implement the function `iterate_f` that runs `f` for `it` +iterations, each time passing the result back into f. +Use `@parametrize` to test the function for the following cases: +``` + x=0.1, r=2.2, it=1 => iterate_f(it, x, r)=[0.198] + x=0.2, r=3.4, it=4 => f(x, r)=[0.544, 0.843418, 0.449019, 0.841163] + x=0.75, r=1.7, it=2 => f(x, r)=[0.31875, 0.369152] +``` + +c) Import and call the `plot_trajectory` function from the `plot_logfun` +module to look at the trajectories generated by your code. The `plot_logfun` +imports and uses your `logistic.py` code. Import the module +and call the function in a new `plot_script.py` file. + +Try with values `r<3`, `r>4` and `3`f` is a function and `x0` and `y0` are two possible seeds. +>If `f` has SDIC then: +>there is a number `delta` such that for any `x0` there is a `y0` that is not +>more than `init_error` away from `x0`, where the initial condition `y0` has +>the property that there is some integer n such that after n iterations, the +>orbit is more than `delta` away from the orbit of `x0`. That is +>|xn-yn| > delta + diff --git a/hands_on_solutions/logistic_fun/single_trajectory.png b/hands_on_solutions/logistic_fun/single_trajectory.png new file mode 100644 index 0000000..174ba96 Binary files /dev/null and b/hands_on_solutions/logistic_fun/single_trajectory.png differ diff --git a/hands_on_solutions/logistic_fun/test_logistic.py b/hands_on_solutions/logistic_fun/test_logistic.py new file mode 100644 index 0000000..f9247f4 --- /dev/null +++ b/hands_on_solutions/logistic_fun/test_logistic.py @@ -0,0 +1,108 @@ +import numpy as np +from numpy.testing import assert_allclose +import pytest + +from logistic import f, iterate_f + +# set the random seed for once here +SEED = np.random.randint(0, 2**31) + + +@pytest.fixture +def random_state(): + print(f'Using seed {SEED}') + random_state = np.random.RandomState(SEED) + return random_state + + + +@pytest.mark.parametrize('a', [1, 2, 3]) +@pytest.mark.parametrize('b', [5, 6, 7]) +def test_addition_increases(a, b): + print(a, b) + assert b + a > a + + + +@pytest.mark.parametrize( + 'x, r, expected', + [ + (0.1, 2.2, 0.198), + (0.2, 3.4, 0.544), + (0.75, 1.7, 0.31875), + ] +) +def test_f(x, r, expected): + result = f(x, r) + assert_allclose(result, expected) + + +@pytest.mark.parametrize( + 'x, r, it, expected', + [ + (0.1, 2.2, 1, [0.198]), + (0.2, 3.4, 4, [0.544, 0.843418, 0.449019, 0.841163]), + (0.75, 1.7, 2, [0.31875, 0.369152]), + ] +) +def test_iterate_f(x, r, it, expected): + result = iterate_f(it, x, r) + assert_allclose(result, expected, rtol=1e-5) + + +def test_attractor_converges(): + SEED = 42 + random_state = np.random.RandomState(SEED) + + for _ in range(100): + x = random_state.uniform(0, 1) + result = iterate_f(100, x, 1.5) + assert_allclose(result[-1], 1 / 3) + +#################################################################### +# These only work after adding the fixture +#################################################################### + + +@pytest.mark.xfail +def test_attractor_converges2(random_state): + for _ in range(100): + x = random_state.uniform(0, 1) + result = iterate_f(100, x, 1.5) + assert_allclose(result[-1], 1 / 3) + + +@pytest.mark.xfail +def test_chaotic_behavior(random_state): + r = 3.8 + for _ in range(10): + x = random_state.uniform(0, 1) + result = iterate_f(100000, x, r) + assert np.all(result >= 0.0) + assert np.all(result <= 1.0) + assert min(np.abs(np.diff(result[-1000:]))) > 1e-6 + + +@pytest.mark.xfail +def test_sensitivity_to_initial_conditions(random_state): + """ + `f` is a function and `x0` and `y0` are two possible seeds. + If `f` has SDIC then: + there is a number `delta` such that for any `x0` there is a `y0` that is + not more than `init_error` away from `x0`, where the initial condition `y0` + has the property that there is some integer n such that after n iterations, + the orbit is more than `delta` away from the orbit of `x0`. That is + |xn-yn| > delta + """ + delta = 0.1 + n = 10000 + x0 = random_state.rand() + x0_diffs = random_state.rand(100) * 0.001 - 0.0005 + + result_list = [] + for x0_diff in x0_diffs: + x1 = x0 + x0_diff + l_x = iterate_f(n, x0, 3.8) + l_y = iterate_f(n, x1, 3.8) + result_list.append(any(abs(l_x - l_y) > delta)) + assert any(result_list) diff --git a/hands_on_solutions/massmail_solution/massmail b/hands_on_solutions/massmail_solution/massmail new file mode 100644 index 0000000..5d79e77 --- /dev/null +++ b/hands_on_solutions/massmail_solution/massmail @@ -0,0 +1,408 @@ +#!/usr/bin/env python +# Script to send mass email +# +# Copyright (C) 2003-2017 Tiziano Zito , Jakob Jordan +# +# This script is free software and comes without any warranty, to +# the extent permitted by applicable law. You can redistribute it +# and/or modify it under the terms of the Do What The Fuck You Want +# To Public License, Version 2, as published by Sam Hocevar. +# http://www.wtfpl.net +# +# Full license text: +# +# DO WHAT THE FUCK YOU WANT TO PUBLIC LICENSE +# Version 2, December 2004. +# +# Everyone is permitted to copy and distribute verbatim or modified +# copies of this license document, and changing it is allowed as long +# as the name is changed. +# +# DO WHAT THE FUCK YOU WANT TO PUBLIC LICENSE +# TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION +# +# 0. You just DO WHAT THE FUCK YOU WANT TO. + +import smtplib, getopt, sys, os, email, getpass +import email.header +import email.mime.text +import tempfile + +from py.test import raises + + +PROGNAME = os.path.basename(sys.argv[0]) +USAGE = """Send mass mail +Usage: + %s [...] PARAMETER_FILE < BODY + +Options: + -F FROM set the From: header for all messages. + Must be ASCII. This argument is required + + -S SUBJECT set the Subject: header for all messages + + -B BCC set the Bcc: header for all messages. + Must be ASCII + + -s SEPARATOR set field separator in parameter file, + default: ";" + + -e ENCODING set PARAMETER_FILE *and* BODY character set + encoding, default: "UTF-8". Note that if you fuck + up this one, your email will be full of rubbish: + You have been warned! + + -f fake run: don't really send emails, just print to + standard output what would be done. Don't be scared + if you can not read the body: it is base64 encoded + UTF8 text + + -z SERVER the SMTP server to use. This argument is required + + -P PORT the SMTP port to use. + + -u SMTP user name. If not set, use anonymous SMTP + connection + + -p SMTP password. If not set you will be prompted for one + + -h show this usage message + +Notes: + The message body is read from standard input or + typed in interactively (exit with ^D) and keywords are subsituted with values + read from a parameter file. The first line of the parameter file defines + the keywords. The keyword $EMAIL$ must always be present and contains a comma + separated list of email addresses. + Keep in mind shell escaping when setting headers with white spaces or special + characters. + Character set encodings are those supported by python. + +Examples: + +* Example of a parameter file: + +$NAME$; $SURNAME$; $EMAIL$ +John; Smith; j@guys.com +Anne; Joyce; a@girls.com + +* Example of body: + +Dear $NAME$ $SURNAME$, + +I think you are a great guy/girl! + +Cheers, + +My self. + +* Example usage: + +%s -F "Great Guy " -S "You are a great guy" -B "Not so great Guy " parameter-file < body + +"""%(PROGNAME, PROGNAME) + +def error(s): + sys.stderr.write(PROGNAME+': ') + sys.stderr.write(s+'\n') + sys.stderr.flush() + sys.exit(-1) + +def parse_command_line_options(arguments): + # parse options + try: + opts, args = getopt.getopt(arguments, "hfs:F:S:B:R:e:u:p:P:z:") + except getopt.GetoptError, err: + error(str(err)+USAGE) + + # set default options + options = { + 'sep': u';', + 'fake': False, + 'from': '', + 'subject': '', + 'bcc': '', + 'encoding': 'utf-8', + 'smtpuser': None, + 'smtppassword': None, + 'server': None, + 'port': 0, + 'in_reply_to': '', + } + + for option, value in opts: + if option == "-e": + options['encoding'] = value + if option == "-s": + options['sep'] = value + elif option == "-F": + options['from'] = value + elif option == "-S": + options['subject'] = value + elif option == "-B": + options['bcc'] = value + elif option == "-R": + options['in_reply_to'] = value + elif option == "-h": + error(USAGE) + elif option == "-f": + options['fake'] = True + elif option == "-u": + options['smtpuser'] = value + elif option == "-p": + options['smtppassword'] = value + elif option == "-P": + options['port'] = int(value) + elif option == "-z": + options['server'] = value + + if len(args) == 0: + error('You must specify a parameter file') + + if len(options['from']) == 0: + error('You must set a from address with option -F') + + if options['server'] is None: + error('You must set a SMTP server with option -z') + + if options['sep'] == ",": + error('Separator can not be a comma') + + # get password if needed + if options['smtpuser'] is not None and options['smtppassword'] is None: + options['smtppassword'] = getpass.getpass('Enter password for %s: '%options['smtpuser']) + + # set filenames of parameter and mail body + options['fn_parameters'] = args[0] + + return options + +def parse_parameter_file(options): + pars_fh = open(options['fn_parameters'], 'rbU') + pars = pars_fh.read() + pars_fh.close() + + try: + pars = unicode(pars, encoding=options['encoding']) + except UnicodeDecodeError, e: + error('Error decoding "'+options['fn_parameters']+'": '+str(e)) + + try: + options['subject'] = unicode(options['subject'], encoding=options['encoding']) + except UnicodeDecodeError, e: + error('Error decoding SUBJECT: '+str(e)) + + try: + options['from'] = unicode(options['from'], encoding=options['encoding']) + except UnicodeDecodeError, e: + error('Error decoding FROM: '+str(e)) + + if options['in_reply_to'] and not options['in_reply_to'].startswith('<'): + options['in_reply_to'] = '<{}>'.format(options['in_reply_to']) + + # split lines + pars = pars.splitlines() + + # get keywords from first line + keywords_list = [key.strip() for key in pars[0].split(options['sep'])] + + # fail immediately if no EMAIL keyword is found + if '$EMAIL$' not in keywords_list: + error('No $EMAIL$ keyword found in %s'%options['fn_parameters']) + + # check that all keywords start and finish with a '$' character + for key in keywords_list: + if not key.startswith('$') or not key.endswith('$'): + error(('Keyword "%s" malformed: should be $KEYWORD$'%key).encode(options['encoding'])) + + # gather all values + email_count = 0 + keywords = dict([(key, []) for key in keywords_list]) + for count, line in enumerate(pars[1:]): + # ignore empty lines + if len(line) == 0: + continue + values = [key.strip() for key in line.split(options['sep'])] + if len(values) != len(keywords_list): + error(('Line %d in "%s" malformed: %d values found instead of' + ' %d: %s'%(count+1,options['fn_parameters'],len(values),len(keywords_list),line)).encode(options['encoding'])) + for i, key in enumerate(keywords_list): + keywords[key].append(values[i]) + email_count += 1 + + return keywords, email_count + +def create_email_bodies(options, keywords, email_count, body): + try: + body = unicode(body, encoding=options['encoding']) + except UnicodeDecodeError, e: + error('Error decoding email body: '+str(e)) + + # find keywords and substitute with values + # we need to create email_count bodies + msgs = {} + + for i in range(email_count): + lbody = body + for key in keywords: + lbody = lbody.replace(key, keywords[key][i]) + + # Any single dollar left? That means that the body was malformed + single_dollar_exists = lbody.count('$') != 2 * lbody.count('$$') + if single_dollar_exists: + raise ValueError('Malformed email body: unclosed placeholder or non-escaped dollar sign.') + + # Replace double dollars with single dollars + lbody = lbody.replace('$$', '$') + + # encode body + lbody = email.mime.text.MIMEText(lbody.encode(options['encoding']), 'plain', options['encoding']) + msgs[keywords['$EMAIL$'][i]] = lbody + + return msgs + +def add_email_headers(options, msgs): + # msgs is now a dictionary with {emailaddr:body} + # we need to add the headers + + for emailaddr in msgs: + msg = msgs[emailaddr] + msg['To'] = str(emailaddr) + msg['From'] = email.header.Header(options['from']) + if options['subject']: + msg['Subject'] = email.header.Header(options['subject'].encode(options['encoding']), options['encoding']) + if options['in_reply_to']: + msg['In-Reply-To'] = email.header.Header(options['in_reply_to']) + msgs[emailaddr] = msg + + return None + +def send_messages(options, msgs): + server = smtplib.SMTP(options['server'], port=options['port']) + + if options['smtpuser'] is not None: + server.starttls() + server.login(options['smtpuser'], options['smtppassword']) + + for emailaddr in msgs: + print 'Sending email to:', emailaddr + emails = [e.strip() for e in emailaddr.split(',')] + if len(options['bcc']) > 0: + emails.append(options['bcc']) + if options['fake']: + print msgs[emailaddr].as_string() + else: + try: + out = server.sendmail(options['from'], emails, msgs[emailaddr].as_string()) + except Exception, err: + error(str(err)) + + if len(out) != 0: + error(str(out)) + + server.close() + +def test_dummy(): + pass + +def test_parse_parameter_file(): + expected_keywords = {u'$VALUE$': [u'this is a test'], u'$EMAIL$': [u'testrecv@test']} + with tempfile.NamedTemporaryFile() as f: + f.write('$EMAIL$;$VALUE$\ntestrecv@test;this is a test') + f.flush() + cmd_options = [ + '-F', 'testfrom@test', + '-z', 'localhost', + f.name, + ] + options = parse_command_line_options(cmd_options) + keywords, email_count = parse_parameter_file(options) + assert keywords == expected_keywords + +def test_local_sending(): + parameter_string = '$EMAIL$;$NAME$;$VALUE$\ntestrecv@test.org;TestName;531' + email_body = 'Dear $NAME$,\nthis is a test: $VALUE$\nBest regards' + email_to = 'testrecv@test.org' + email_from = 'testfrom@test.org' + email_subject = 'Test Subject' + email_encoding = 'utf-8' + + expected_email = email.mime.text.MIMEText('Dear TestName,\nthis is a test: 531\nBest regards'.encode(email_encoding), 'plain', email_encoding) + expected_email['To'] = email_to + expected_email['From'] = email_from + expected_email['Subject'] = email.header.Header(email_subject.encode(email_encoding), email_encoding) + + with tempfile.NamedTemporaryFile() as f: + f.write(parameter_string) + f.flush() + cmd_options = [ + '-F', email_from, + '-S', email_subject, + '-z', 'localhost', + '-e', email_encoding, + f.name + ] + options = parse_command_line_options(cmd_options) + keywords, email_count = parse_parameter_file(options) + msgs = create_email_bodies(options, keywords, email_count, email_body) + add_email_headers(options, msgs) + assert msgs['testrecv@test.org'].as_string() == expected_email.as_string() + +def test_malformed_body(): + parameter_string = '$EMAIL$;$NAME$;$VALUE$\ntestrecv@test.org;TestName;531' + email_body = '$NAME$VALUE$' + email_from = 'testfrom@test.org' + email_subject = 'Test Subject' + email_encoding = 'utf-8' + + with tempfile.NamedTemporaryFile() as f: + f.write(parameter_string) + f.flush() + cmd_options = [ + '-F', email_from, + '-S', email_subject, + '-z', 'localhost', + '-e', email_encoding, + f.name + ] + options = parse_command_line_options(cmd_options) + keywords, email_count = parse_parameter_file(options) + with raises(ValueError): + msgs = create_email_bodies(options, keywords, email_count, email_body) + +def test_double_dollar(): + parameter_string = '$EMAIL$;$NAME$;$VALUE$\ntestrecv@test.org;TestName;531' + email_body = 'Dear $NAME$,\nyou owe us 254$$' + email_to = 'testrecv@test.org' + email_from = 'testfrom@test.org' + email_subject = 'Test Subject' + email_encoding = 'utf-8' + + expected_email = email.mime.text.MIMEText('Dear TestName,\nyou owe us 254$'.encode(email_encoding), 'plain', email_encoding) + expected_email['To'] = email_to + expected_email['From'] = email_from + expected_email['Subject'] = email.header.Header(email_subject.encode(email_encoding), email_encoding) + + with tempfile.NamedTemporaryFile() as f: + f.write(parameter_string) + f.flush() + cmd_options = [ + '-F', email_from, + '-S', email_subject, + '-z', 'localhost', + '-e', email_encoding, + f.name + ] + options = parse_command_line_options(cmd_options) + keywords, email_count = parse_parameter_file(options) + msgs = create_email_bodies(options, keywords, email_count, email_body) + assert msgs['testrecv@test.org'].get_payload(decode=email_encoding) == expected_email.get_payload(decode=email_encoding) + + +if __name__ == '__main__': + options = parse_command_line_options(sys.argv[1:]) + keywords, email_count = parse_parameter_file(options) + msgs = create_email_bodies(options, keywords, email_count, sys.stdin.read()) + add_email_headers(options, msgs) + send_messages(options, msgs) diff --git a/hands_on_solutions/numerical_fuzzing/test_var.py b/hands_on_solutions/numerical_fuzzing/test_var.py new file mode 100644 index 0000000..f19affe --- /dev/null +++ b/hands_on_solutions/numerical_fuzzing/test_var.py @@ -0,0 +1,22 @@ +from math import isclose + +import numpy + + +def test_var_deterministic(): + x = numpy.array([-2.0, 2.0]) + expected = 4.0 + assert isclose(numpy.var(x), expected) + + +def test_var_fuzzing(): + rand_state = numpy.random.RandomState(8393) + + N, D = 100000, 5 + # Goal variances: [0.1 , 0.45, 0.8 , 1.15, 1.5] + expected = numpy.linspace(0.1, 1.5, D) + + # Generate random, D-dimensional data + x = rand_state.randn(N, D) * numpy.sqrt(expected) + variance = numpy.var(x, axis=0) + numpy.testing.assert_allclose(variance, expected, rtol=1e-2) diff --git a/hands_on_solutions/numpy_equality/test_numpy_equality.py b/hands_on_solutions/numpy_equality/test_numpy_equality.py new file mode 100644 index 0000000..54055f8 --- /dev/null +++ b/hands_on_solutions/numpy_equality/test_numpy_equality.py @@ -0,0 +1,23 @@ +import numpy as np +from numpy.testing import assert_allclose, assert_equal + + +def test_equality(): + x = np.array([1, 1]) + y = np.array([2, 2]) + z = np.array([3, 3]) + assert_equal(x + y, z) + + +def test_equality_with_nan(): + x = np.array([1, np.nan]) + y = np.array([2, np.nan]) + z = np.array([3, np.nan]) + assert_equal(x + y, z) + + +def test_allclose_with_nan(): + x = np.array([1.1, np.nan]) + y = np.array([2.2, np.nan]) + z = np.array([3.3, np.nan]) + assert_allclose(x + y, z) diff --git a/how_I_compiled_qcachegrind_on_osx.txt b/how_I_compiled_qcachegrind_on_osx.txt new file mode 100644 index 0000000..a324dda --- /dev/null +++ b/how_I_compiled_qcachegrind_on_osx.txt @@ -0,0 +1,30 @@ +1) Install dependencies with MacPorts: + sudo port install qt4-mac graphviz + +Get source code for qcachegrind: + +2) Get kcachegrind-0.7.4.tar.gz from http://kcachegrind.sourceforge.net/html/Download.html + +3) Unzip it: + tar xfz ~/Downloads/kcachegrind-0.7.4.tar.gz + +We need "qmake" to find the right libraries + +4) Set PATH to find the right "qmake": + export PATH=/opt/local/libexec/qt4/bin:/opt/local/bin:/opt/local/sbin:$PATH + +5) Set library path: + export DYLD_LIBRARY_PATH=/opt/local/libexec/qt4/Library/Frameworks/ + +Compile: + +6) Compile: + cd kcachegrind-0.7.4/ + cd qcachegrind/ + qmake -nocache + make + mv qcachegrind.app /Applications/ + +Done! + +See also http://blogs.perl.org/users/rurban/2013/04/install-kachegrind-on-macosx-with-ports.html diff --git a/material/code.py b/material/code.py new file mode 100644 index 0000000..0f87260 --- /dev/null +++ b/material/code.py @@ -0,0 +1,106 @@ +""" +This is code that is copy-and-pasted in the slides. +""" + + +def test_arithmetic(): + assert 1 == 1 + assert 2 * 3 == 6 + +def test_len_list(): + lst = ['a', 'b', 'c'] + assert len(lst) == 3 + +def test_various(): + assert 'Hi'.islower() + assert 2 + 1 == 3 + assert [2] + [1] == [2, 1] + assert 'a' + 'b' != 'ab' + + +def test_1_and_2(): + assert 1 + 2 == 3 + +def test_1_and_2_float(): + assert 1.1 + 2.2 == 3.3 + + +from math import isclose + +def test_floating_point_math(): + assert isclose(1.1 + 2.2, 3.3) + +def test_floating_point_math2(): + assert isclose(1.121, 1.2, abs_tol=1e-1) + assert isclose(1.121, 1.2, abs_tol=1e-2) + +def test_floating_point_math3(): + assert isclose(120.1, 121.4, rel_tol=1e-1) + assert isclose(120.4, 121.4, rel_tol=1e-2) + +import numpy + +def test_numpy_equality(): + x = numpy.array([1, 1]) + y = numpy.array([2, 2]) + z = numpy.array([3, 3]) + assert x + y == z + + +from py.test import raises + +class SomeException(Exception): + pass + + +do_something = do_something_else = lambda : 1 + + +def test_raises(): + with raises(SomeException): + do_something() + do_something_else() + + +def test_raises2(): + with raises(ValueError): + int('XYZ') + + +def test_lower(): + # Given + string = 'HeLlO wOrld' + expected = 'hello world' + + # When + output = string.lower() + + # Then + assert output == expected + + +def test_lower_empty_string(): + # Given + string = '' + expected = '' + + # When + output = string.lower() + + # Then + assert output == expected + + +def test_lower1(): + # Given + # Each test case is a tuple of (input, expected_result) + test_cases = [('HeLlO wOrld', 'hello world'), + ('hi', 'hi'), + ('123 ([?', '123 ([?'), + ('', '')] + + for string, expected in test_cases: + # When + output = string.lower() + # Then + assert output == expected diff --git a/material/logistic_map_plots.ipynb b/material/logistic_map_plots.ipynb new file mode 100644 index 0000000..8d7278c --- /dev/null +++ b/material/logistic_map_plots.ipynb @@ -0,0 +1,217 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 13, + "id": "fecaca5d", + "metadata": {}, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "def plot_style(figsize=(12, 6), labelsize=20, titlesize=24, ticklabelsize=14, **kwargs):\n", + " basic_style = {\n", + " 'figure.figsize': figsize,\n", + " 'axes.labelsize': labelsize,\n", + " 'axes.titlesize': titlesize,\n", + " 'xtick.labelsize': ticklabelsize,\n", + " 'ytick.labelsize': ticklabelsize,\n", + " }\n", + " basic_style.update(kwargs)\n", + " return plt.rc_context(rc=basic_style)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "21292898", + "metadata": {}, + "outputs": [], + "source": [ + "def logistic_map(x, r):\n", + " return r * x * (1 - x)\n", + "\n", + "def iterate_map(x0, r, n):\n", + " xs = [x0]\n", + " for _ in range(n):\n", + " x_np1 = logistic_map(xs[-1], r)\n", + " xs.append(x_np1)\n", + " return xs" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "id": "c2de665f", + "metadata": {}, + "outputs": [], + "source": [ + "x = np.linspace(0, 1, 100)\n", + "r = 1.5\n", + "f_x = logistic_map(x, r)" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "id": "e4f218ce", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "with plot_style(figsize=(5, 5), titlesize=20):\n", + " plt.plot(x, f_x)\n", + " plt.plot([0, 1], [0, 1], 'r--', lw=1)\n", + " plt.xlim(0, 1)\n", + " plt.ylim(0, 1)\n", + " plt.xlabel('x')\n", + " plt.ylabel('f(x)')\n", + " plt.title(f'r = {r}')" + ] + }, + { + "cell_type": "code", + "execution_count": 84, + "id": "3b666ffc", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "r = 1.5\n", + "xs_01 = iterate_map(x0=0.1, r=r, n=20)\n", + "xs_03 = iterate_map(x0=0.3, r=r, n=20)\n", + "xs_05 = iterate_map(x0=0.4, r=r, n=20)\n", + "with plot_style(figsize=(5, 5), titlesize=20):\n", + " plt.plot(xs_01, lw=3, label=0.1)\n", + " plt.plot(xs_03, lw=3, label=0.3)\n", + " plt.plot(xs_05, lw=3, label=0.5)\n", + " plt.ylim(0, 1)\n", + " plt.xticks([0, 5, 10, 15, 20])\n", + " plt.xlabel('iteration')\n", + " plt.ylabel('x')\n", + " plt.title(f'r = {r}')\n", + " plt.legend(title='$x_0$ value', fontsize=14, title_fontsize=16, frameon=False)" + ] + }, + { + "cell_type": "code", + "execution_count": 85, + "id": "782fd773", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "r = 3.2\n", + "xs_01 = iterate_map(x0=0.1, r=r, n=20)\n", + "xs_03 = iterate_map(x0=0.3, r=r, n=20)\n", + "xs_05 = iterate_map(x0=0.4, r=r, n=20)\n", + "with plot_style(figsize=(5, 5), titlesize=20):\n", + " plt.plot(xs_01, lw=3, label=0.1)\n", + " plt.plot(xs_03, lw=3, label=0.3)\n", + " plt.plot(xs_05, lw=3, label=0.5)\n", + " plt.ylim(0, 1)\n", + " plt.xticks([0, 5, 10, 15, 20])\n", + " plt.xlabel('iteration')\n", + " plt.ylabel('x')\n", + " plt.title(f'r = {r}')\n", + " plt.legend(title='$x_0$ value', fontsize=14, title_fontsize=16, frameon=False)" + ] + }, + { + "cell_type": "code", + "execution_count": 86, + "id": "dd04eb9b", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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wVwCAO/bfgUQggQu3X9j/A1HVhhqaopwBwptz1OPc0tPcfYokoVKvIOwPr8MRdY8FgToaaBh2JIIJS69hVMtbrxalldTz3H15BwYkmqbhnV96CI/PpgEA//XC4/Dnbzmp28NzjJJSwtef+zqKtSKuPPlKjEZG1+1Y3MDsCq89yJYVjG/O5cERvEz4KMTu2d3M7fsP378ux4H8PCCqLW5iWvDICr+4A0DeQUvPRkCtXsMyMerQYcewwzAIr1MmvCKo/+ZsZPY6npvLNQMwAHzzV5TZ6S8+dd8n8X8e+z/48lNfxnv/8/ehapu3tAMAs6JMuPzyyoS9IHwUYrnEKpAzlYzBM3sMjopewyYWZ80btCPlCvN9PhJ3sFRaMnwsX7MRhDcYHb2c5c+9vGJfeXskzWZqy4UqavX1CXzVehU/mb27eftg/hD2r+xbl2NxC7MrHh3tBeGjECvlFea201pY16CiLB0OM+Hn5rK444kjWBWocPuFI0VxsM3n7ffVbgSIlNE67PhHb7QgvCLYFGVV++fNcoEXnK1XkDi0egA0/K8uPLEux+IWZlfFdPTLCV5N+CgEDcK5qphu7DmMTCwcZMJ3P7eAD/zfR1FXNYwlQvjJx87HYDTY5QHax1xlRXh/ziSj3MgwC8J2KPaFDVYTXi4vAwFyLJr94Lks2PBlywpG4iGnh+YYs/OP8sciULZvFmia5gmz4GXCRyU2TiZsREenbb/U7b+cQV1tKFOXchX8+Jn1oX/nDEws8pvUhERk1KGjWLL+mYwy4WpdRUXpc8uJpmFFsPHMOaifLuf5IJxZpyAxm3qGuy+7iYeHLOUrKNf438SrCXvY1KjUK1wt72igow+T2pxoYk+vUa1XsSSJA0qhvNrno3EHoh5hHXmLQVjTNMM+YQAoVPochMtprIB/z7xkv71oOc9/rvUKwjMCsVl2k553gFgZDQDZ0suLjvaC8FGGVcFFmavm1qe/MeOeMCtFMpJ0qf914YWcuJ8WAHLEynKzYDF70PAxq3T0SqGKqolYqe+UdHoGKz4ffxwSoNowIAHEdPS6ZcICPUJ2k553gLhHGPAyYQ+bHJSKBgBVUx0Nae8KmmZMR9vMhFVVw2qRXQwzxf5fqEcEPcI6Nqsbk1kmXLC4wM918PvtuzgrPYMVH7+0aZKEQkHcE20EuvkD1q9mOVvjz7Hseuk9XIBIGQ14NWEPmxyiIAysAyVdSAFGQwBsZsKZUq1ZD9aRXocLdW55j+FjOYNe242ORZOaYt7iOSMa3MC8zroEYT4TBoBc/oitl9oodLSiKjgsEJZl+725dhFGdPR6+o2vB7wgfJRhwwRhs/F+ZXt9y6I2kXSx/3T0XOZFw8ecuDGtN1RNxaLJ5qFg0azDSJSlI1/pb9Aqr76Igixe2nI2MmFN04RDKdYjU5vPzkKR+PuzDqZdbRSIjDoAj472sMmxUjJooek3bWUkygJs09EiSnBdMmGTLCq/CRfDlfIKFBhrBfI1aw5TRu1JOvqd2ayuGk9LshOEsyUFisp/P+uRCYvakwAgq27eMZozHh0NwAvCRx0MM+F+1yyN6sGAbTpa2CayHjXhsrFaOFfffHNQzXqEAaBYt7ax6JQJ91sdvWIioLOq+AaAlICBAdYnU5tdfEp4f9bmyMmNAqWuGmoJXm5mHV4QPsqwbBAo+k9HmwRhmxuCFREdXar1XfE9rxjTs3bn724EmPUIA0De4sZi3qQ9CegzHa1pWDb5XDmDTaoIos0fsD6Z8Ex6v/D+LOehtTkwlylzOg8dXibsYVNjw9SEzehom5mwiI6uq1pfBT+qpmJOM36/gsljGxWLeXPDk0LdWt19PmOeMfe1Ram0ihXN+LhzNoxiRKIsYJ3o6IJYxZ7dpGM0jZTRAFBR1JfVTGEvCB9lEPUJA+sRhE0y4WoOsNGvKRJmAUC6j5T0SnEZVYEwRkdO23yLxgLJrobr7GfIW9xY0AlK24Yi7Ov0k442aE9qHouN6yBl4FG+LplwNS28vy5JKG7C+dxGoiwdLyeFtBeEjzJsiJqwpplnwoAtSnoj0IKiOcLtcOLGtN5YzLK/0Y4q+30WUO+YZZWqda6Gd9xYnLndVzrapD0JsCdQNMqE++3opGkaDplk91mTGvhGhVF7ko71UkjfefBOfPWZr+KhuYcMExq34QXhowiaphkGYad9rI++tIKf7VmEYmd8WzndyHZNn2MjCG+AjGRu+TnmtkyCU0WSUKtvrlrWAqE4d9bY41fQsEE1g0iU9YpxGoT7GLTSM1iRTYKwjZnCovYkoBEgVIN6Zi+wlJ9D2YSFyebs9T5vBGzUTPg/XvgPfO6Rz+H9d70f5//b+fjiE1/s+Xt6U5SOIhSVouGi6SQT/se79+HzP9kLADj/hDH86x+dZe0POSpaAiQJaDfQt5UJrz8dPbf6AnN7u6LgYIAd05MrrWA4PtG3Y+oWC2Snv1NQhyvUCgj7w4avQanoRMiP8QQ7YaivC2oHOjpno5XMiIHRNCBXUTAQCQgfdxuzc4+YPp7dhLOszWrCwPqJs55feZ65fUzymJ6/p5cJH0Uw6hEGnNWEb/35wea/79u7hBcWLWbTlIpOTAGhBHufDcMOo0y4n/7Rc7lDzO3jJT4w5TfRYqhpGhaI2ntneIx7Xie7U+qWNTEQRjzM7u0Lfc2EX8KyCR2d75DZtyNlsPkD+hskZgzak3RkbVpxbgSI5gi3Yz3o6FQphRRxkDtx+MSev68XhI8iGLUnAfbNOopVhaPjOl04TdD2pMHtQGiAvc8iHV2rq4YZbz8z4SNkXvCOyCT8hJLOdVAbbyTkajmUSHvL9PAJ3GfKdzhvKB09mQwjHmKDcN/paLNMWLW+cTPa/AH9LYXMpl8wfXyzjTMs1+pYyrEbHHrOrMckJZoFR/wRbE9s7/n7ekH4KIJRPRiwnwmLqDh64RiCZsKD00CYBGGLdDQd3NCOfi6E86SmviU5jTipCxaKm2cxXBRkT+OTZyCusoG504hGSkdPDoSRIJlw31qUNA1aJ2GWDRW7URkE6G8mPJs3F15ttnGGoulJp0wlmdvrkQnvWWG94Y8fOh4+E32BW/CC8FEEMzWf3ZqwiIozo+cYcEF4OxBmLzKrmbBRXQ7or3/0EY397FODOxAn2pzcJspIqChruF5HaOoMxMjGIl9gGQAKLggnw4gF2SCc61cmXFpFVilAkYxVTDnJmsBQqatYNWFa+poJV8yDbGaTjTOkyujhWBATA2x5Zz1qwjQTPmnopL68rxeEjyKYZcJVtdpR6doOUfBL5SwGPUpHD0wDIRKEK9ZqwuZBuD8XarFaQIas61PDJyIhsZdPfhNlJAsr+5jb40odmDgVMZIJd7J5pHS0UU24L4YS6ZdMs2AAsNpRaxaAgf4G4RmN/Y63KOymZrONM6TK6OmhCJLknFmXTHiVzYT7UQ8GvCB8VMEsCAP2smFRe8aS40x4WpAJWwzCBkYdQP+GOND2JACYmjgdcdDaZ7ovx+MGFlZZo44JVQMGtiFOnlfocE5RYdZkMoxEiFUNqxpQ6ocDUof2JACoyBKqlc6h2Oy8A/oXJDLFZeTIBvBUiTVD2WzjDKkyettwFEmiNO93TbhYK+Jg5iBz38nDJ/flvb0gfBTBTJgF2KsLi8zrU1ZqwpUcUCIZ4eAxfCbsAh3dryEOc0SdOlyvIzx4LGI+0qLU7yEZXWCBqL3HfRFAkhADG8TMasJ1VcMiOScmk3wmDPSpLiwQZUX9Ee5pubzYArIdZucd0L9MeIZMT/JpGk6MTzP3ZS0O2tgooHT09FAUyTC5lvqcCe9L74PWNlFMlmS8YugVfXlvLwgfReiUCdtzCxLQ0VYyYZFd5cA2x8Is80y4PzXhI6RHeErzAT4/EjLbD9tJSbyRsEgmKE2EBgEAcZldDAsmv9NyvsKZ8E8MhBAL8dloXxTSAlHWMQJ1q5Ug3Olc71cQnl18grm9pa5iKLGNuS+3ycYZcnT0cATJCKWj+5sJ03rwscljERFs4HoBLwgfRehIR9vIhEXKUEt0NK0Hx8aAQKRHwqw+ZcLE3nHK17g44/4oc39e2Ty04EKVLQdMRMYBADE5yNxvtrGg9WC/LGE0FkLI70OQZKR9CcKrL3GZ8GR8C4K07cpCX22nTLhfdOnMyl7m9rQUQjIyzB6Lurl8likdLcqE+y3MosroftWDAS8IH1UwM+sAgIxFMRQg7pFMF2uodbKvFCmjAYEwy1oQFk1Qar5En6atzJGscSo0BACIB9ggbMeNab2xUGcXwvFkg+KM+1iVaqFmXD+l82AnkmHIcqOASSnpftHR1KhjODyMODllrfTVdqoJ9y0TJr7Q06EhJCMjzH2baZxhplTjstxpUU24z3Q0p4we7o8yGvCC8FEDVVORJsKgWCDG3O6Wjja7vwkahAfW6lcOhVmiWcLt6MdiOEeyxqlow5oyEWBlTAUb6vP1RFkpI0MW7smh4wDwNdS8idcy55aVbNHzlJLueZvS2tAQSkcPh4eRBKts6qT4BvjzPOhnl8q+BeEKe6zTsS0YiI4z922mcYY0C5YkYMtgmFdH91GYVVfr2LvKMg79ak8CvCB81CBbyaJOjAiOTR7LPscOHW0Q/DoadojcsgDHjllmrkVAfyjpOSJ82bLmJxsPshsLO25M64lFwdD78dFTAPDZfUHhBzToEBl16IiHaG25x4tqcQWoFbAis0vaSGQEcYlsCCy0ktHzbscIu6HtF106QxiL7YPHIRmfZO5TJAml6uYohVCjjslkGCG/j8uES7U6qkp/MvyXci+hXGfP5ROGT+jLewNeED5qIKoHb0+yohSrQVjTNMOMt6M4y4iOdirM6pB599qwQ1EVLBKDh8m1CzRBNhZ5dXNMUVogdcaYqiI+0vhM8QDr8W2W3XM9wslWEE7027oy/RIAcJnwSHgECVrntlCWoZqIHaMkCPeBLi1WclgmK/T0+C4kE1u552aJ2n2jQqSMBsC5rAH9U0hTKnosMobRyGhf3hvwgvBRA9qelAgkMBJma0dW6ehsSYFiMKqtoziLqqON6OhaEegw+q9cq3OLNzVD6nWv8NLKftTJm24ZPw0AEAsPMffnN0ltbmGZFaFMKHUg0ciuYtzGwniTI+oR1kFrwj2fpLS2+aPCrOHwMOIkCFu5DmgmvHOMDcKZUq3nFPDs/GPcfdu2vBZxYRDeHDOFqTJ623Cj/EGFWUD/FNLrKcoCvCB81IBmwsORYSSJGMqqWYeoR1iHKR1dKwFUeWokzAIaPcUmEBmG6DtnHb3uFT5CWkTCqorB0UYTfyJKNjnYHHW5xfSLzO1xKQCsmVzECWNRMPFaNqOjY6E+T1JKz6AGICOoCSdInTtnIjbTQRmYnWNs/b9W13puQDK78Dhze1ypIzwwDV8ojgRxNsvm+RLDRoRIGQ0A4YCPq7v3i/JfT1EW4AXhowZcEA4PI0lqllbpaKNh5kAHOjojoMQGDTJhACinTY+DLoR+WcL2YTYI97pXeI5Qt1OqBCnQECDFCWVVkiUoHbL7jYAFMhBgok1gFgvR7N56EG6no/s+SSn9EtKC6UnDkWEk/GwWm++gYhcxMJSOBnovzpohwWG7FGxSQUmNZWeyxU0ShMkktum265k37PAyYQ+bCHR4gygIW6WjzabHmLUMcfXgyFBrjnAgChCBTCdxFs3Ih2NBDEbZC7XXwqw5YmU31WbQEY9NcM8vWFDerjcWSIvOeFvgjZEe1JLUUI9S5Mo1FKrs/VNtmXDfJykJlNGyJGMgOIB4kM1isx2CsEgMKArCvVbwzubY0s72YIulSIJmjRv/vNM0jRNmTQ+1WAresKP3G9pUKcWV8vqpjAa8IHzUwM1M2CzQLuWM1bLCwQ06JMm2OItmwiPxEB+Ee5yNzBXYGcFTbQthIj7FPT+/CWjBRXIeTMZanyMe5QUpBYEJCa0HA2wm3PdJSukZLBPf6MHQIHyyDwlyHZjVuQFgRcDADEUDnNis15nwLNksTUdbv1NSouYW5h4BGwFL+QrKNTrD2jgT7gcdTbPgiD+C6cS0wbN7Ay8IHyWgQXgoPMTXhC0GYTNFsq1MeJBVZ9t1zaI9wqPxIAYjrMim5zVh8r1ORVo9mtHYBGTqxrQJaMEFYnM4vtZyBQAx0oMKNKZIUcxn2NcYjAYQDrSCoGiSUs+w1iO8LBBlAUBizZJTR04zP2coAzMSD0KSJK6NpudBuM5+79ODO5v/TvpYy9Rs1boRz3qBKqMDPonZuK2HYQcNwicMndCXGcLt8ILwUYJlQkcNh4eRoO0mtQIUCxZ3Zm5BpjVhqoymQdimaxbdDAjp6B7XhOfJQrgl2dolS4EQYiQI5wr9nyn82Mwq/vzbT+AffrK3Y2BQ6jWkSMvVxPDxzX9H42Pc3+SL/Exh2p7UrowG+tyiVFwGakVhexIAJCKkzq2Zq9g5BibWCHgDfQzC1VoZc+R3mh57ZfPfSSI22wzjDCkVvXUwAp/cqm2vh2HHeouyAIBvzvKwKUEz4ZHwCJcJA0C+msdgeND0tcwMMtLFGqqKyikZGw8auGXpoHR0B9csmnWPxEJ9XQg1TcMR1IE2xyXdWUpHXJPQvvzlS3zA6iUWc2X88W0PN+ffpotV/O1vv9Lw+amVF6CSlquJ8dbzfeEhRFUVxTbTi7zA3IN3y2KDcF9tK5s9wuJMOE5tHiVzFTvVRIzEG+wLV7Ps4bl3ePEJaOR3mt7y2ua/k4E4UGt1ImyGcYacMpqILBOUjl6HTLjfoizAy4SPGlipCQPWKGkzYRZgkikbuWXp4IJwh0xYQAsORlk6upfCrGzuCEoy6REeZQNcnFxCVtyY3MT3n5hjBtD/x68Pm/avLiw9zdwOaBqGRtp2/6Ek4qT9pVDks3uuPYkEYdqi1NOacLNHmLQnrYnMklE2uy9IgCoQm+mgm9CRWOOc6+cGkPYID9VVJNo2gMkgy3JthnGGlI7eRtoN+7nJARozhF/KvsTc168Zwu3wgvBRgJpa44LrcHgYIV8IATKazloQNqd4UznB40oVyJERcYMkE7ZJR9NWqdE4T0f3siZ8ZIHtEZY1DeOTpzP3JYjiO9+h7cpt/PgZVjiWLSumTMbiyj7m9rgqQfK3fac+P2Ia9VrmRT90eEN7jzDAtyj1tCZsFIT1TJio2FVJQlFAseugJZeReP/p6FliqDINP9DGTiRJnTu7CXzLRSMM28EJs3qsqBfOEB7szwzhdnhB+ChAWrDwD0eGG2ISBwrpTn7NS3mBQjp7GKC1No6OtjfEga8J83R0rqJ0nuzkEHPLzzG3x1QNgRCbgVA3prwNf+5usZyv4JGDfIA8sGRMTS5k2J3/BDl+AIiRZaEgsETl3LJIEKYtSsVqnZs97BpWzenoBPFaBoB8bp67Twfd/Ol0ND33epmpzZAMbTrAXjvJMBlnqG38cYZcEOYyYdon3NtMmNaDdyR3IOwPGzy7d/CC8FEASkVLkDCw1kpjVyFdVzWsEj9mOhtWmAlTKjqYaPQJt8NGJqxpGslIVDyavgNfevbT8EVfYJ7bq8VwLn2Aub1F4gNWnKhU7Uyq6hZ3P7cIUVzbv2TsCLVYYNmKiQBfsohZyO47CbNoJgz0UJylZ8KyOBOOxfggnC0YB2G6+RtdE2bxmVoPM2GiLdgeZbP5JGkly5qYqmwEKHUVR9LsOUNrwv0WZj23wm6y16MeDHjCrKMCtNl8KDwE354fAPvvQUJhT+RO1pWrxSpoSfEV43E8O9f6O6F/NNeeNM0bPdvIhAvVOiptU1SCI/fh6/vuBABEtsso7P84tFpjIUqXak3K0E3M5Y8wtyeJ2hwAEr4IUG/VgQt9FMhQKlrHAZMgPF9hN2wTAqP6uBwA0PqNC2TjVqurHGVLhVm0Jgw0KGmaTbqC9Aw0GGfCPn8QcVVDvq2+L1J86zASZg3QUkgv6Wglz6RI0wM7mMeT3DjDxsZVotfcBsFcpswxIe1GHUD/W5Q2gjIa8DLhowKcKEsKAt/6A+DR25BcYm0XO2VqonrwiZNs8BH6R3dqTwJsCbPYhbCOwPADzVuSpCKQbNVreyXOOlJmBUlbwoKARUb/5Tq4MbmFfEXB/S+I26H2m9HRxDd5PL6Fe06MZPeFKvs3S7kKt1HrVBPWj9l1rPUIlyQJZTrGsG2ASZwcb64k/u40TUOqwLfGAf2rCdfrCg5JbGY7vTZqUgcdZ1iTJJQ3cJsSpaKjQV/ze9XRT7MORVW4GcLrlQl7QfgowAoRzgzXWgEsSY3eO9DRNAsYjAa4LEfYK2zmlqXDBh3dXpf2xfdC9rOBQA63ssBMj3qF50nAmhJMr6Gj//J9Esjct3fJcN6qWSa8qLHf1cTAsdxz4j72986T7J5S0UG/jCGSJfpkCdEgnePbgyBcSAFKiTPqAFrqaIAX0OVKYhV7vqJw3+toXExH9yoIzy89A4W2J029hrmdFGyeslnr4wy/8sCLeNPnd+OD//cRLJq54LmEQ4IRhjRrHyDq6EK1DqVHeo+Z7Awq5Fo9ccgLwh4cgsuE2wIvN22lQxCmWcBILIixBJsZCYOwiI6msOGY1Z6RBwb4kW6+UKu22bNMmDgrTQ3s5J4TJ60inSwR3YIRFQ0AMytFVBS+RqgVV7FIssXxEX7hiZHsvqCwWcwCN7ghJKRBKSXdk0zYQBkd8oUQ9bc+R0KioxXFNo8iJqjVJ0wztd7ULGfmHmFux1QVwyQTTiS3cX+XJeUTIzz4Qgp/+4NncWCpgB8/s4DP/3hv5z/qEp2U0QDfJwz0bogD7Q8ej4xjhPST9wubOgg//PDDuPTSSzE0NIRYLIazzjoLt99+u63XSKfT+Ju/+Rvs2rULiUQCo6OjeO1rX4ubbroJ5XLvd4hugAvCtVbwoJlwZzqa1MNiIYzGWdpITEd3sKwEgJB17+jmcchF+OPPco9LwWVAaiyYvQjClXIGyz42sEyN8j2EdPRfJ0tEN1BVVNyzZ9HwcVUDZpaL3P3p1LOokr7nyTHe2CNGpw7V2euAtidNJfkFFeBds3rSptQ06uBFWe0bgwSnYhdfB7QzIBLwIbrmg03p6FKtbshGdINZosqf1nyQyOfzBaNcP3c2b7wxa8etD7KjLO/es9j72cjEqIP2CANGM4V7cz3tWV1/kw4dmzYI7969G+eddx7uv/9+XHHFFfjwhz+MVCqFd7/73fj0pz9t6TXS6TRe/epX44YbbsDAwAA++MEP4l3vehdWV1dx9dVX47LLLoOq9oYOcRPcBKVqi/oZIHROJ2GWqD1jLE4zYZItqPVGi1I7BkQ1YZIJK2VAEdO3+mIYSD4JSeazOknSIIcai04vhjjMkx5hAJiaPIO7L8GN/uv9+fLQgWUuQ6A1WJFCemGJ3czImoaRBD+EIk7asAp19vfm3LIGxG0dfXHNaiqjjevBAE+xG21GjURZAB+Egd5Q0rMZNkhO+3lBICAYZ0hneQtwOF3iNnCpfIUrMbgNsxGGOsIBGQGy8e0V27BRRFnAJlVHK4qC973vfZAkCffddx/OPPNMAMC1116Lc845B9deey3e/va34/jjjzd9nS996Us4cOAAPvaxj+Ef/uEfmvdXq1Wcd955uOeee/DAAw/g/PPP7+nn6Rbc8IZyawG2TUdzk4t4OjpTqqGi1BHyr+3Oc3MA9aS2IswCGpS0wK9YpwUDg48aHqsvPAe1vL0nAo4jxFkqoWqIC/pN6dShPHqbUQA8FX3G9CDCARkPHWidByJx1uLqfub2CHycmQsAxEhveYFk93x7kliZTjcGPXHNMsqEyUjGhD8CtL19TjAZChC4ZbVtQKmjE9C4Fuj10S1mS2yQnBYM1QCAJHw40rbpszLO8Bu/nBG2tT15KIOpATGj4QY4y8oh/r0kSUIyHGB+g15kwpqmmdtVVvJAKI5+YVNmwvfccw/279+PK6+8shmAASCRSOBTn/oUFEXBrbfe2vF1Dhxo9IFeeumlzP3BYBBvfvObAQCLi513l+sN2qI0Um2d8O7Q0fwiw9TOqDLaHwFivJKYE2YBhpT0cqECKbgEX2RW+DgAyGt14XTR/TrsfJoNWFsgnqxCg3AnS8RuoaoafvIs6+X8llMncdwYu2iIMuH5LFsymPCJF914mM3uCxr7eahlJRXu6aA14d7Q0XpNWNyepCMRIBS7gYqdnv+jbQrekN+HcIDM8e1BkJipsdfo9rYpV+1IUje8DpapVUXFNx8WX09PHerdFKZyrY5FUsLaPsJnwkB/DDtSpRSXuDQz4fQM8A8nA3f+FZDvjw/8pgzCu3fvBgBccskl3GP6fffee2/H1zn11FMBAHfeeSdzf61Ww09/+lNEIhGcc845XR5t78HVhOutRdO2OlpgFTkQCcBPaomMOIsb3LCN7xEGgEAY8BHDC4Ne4eV8FYEB4ywYAOTwWhDuRSZMlKZTpE6qI0GyFE2SUOzhgPVfz6a5Be0tp05gJwnCItesBTJmcTwoYCYAxEgAoxR7J7csHX2ZpLR27i0bWFbqoCr2nIGKnTJBtI2m121KmqriENjvafuI2M84KZNxhpW06Wv/5NkFwyloTx7uXRA+tMpveKhblo5+GHaYzhC+7+8bicFD/x/wf3YBuz/j+vtTbEo6et++hv+tiG4eGhrC6Oho8zlmeN/73of/+3//Lz7/+c/jkUcewWtf+1pUKhXceeedWF1dxe23346tW/m2FB2VSgWVSuukzmb7Z1moo1grokR29cNtdWBRJmzW1E9rwsOxEGRZwmg8xNCQzMWcsSDK0hFKAu0DAQyC8FK+hMDAr5n7jhs4DvszrQzVF5oHoPZEmDVHHIumQmLlpIiizueOIB4TU4jd4q5nWSr6FeNx7ByLY4bQffuX8tzvvFhJM1f8hAHNSacOFdqMIDRN6+iW1XydMFUku7ygrvUIA8a+0ToSRBSYU8XnjBkdDTSC8EK27Zp3OQinVvZxQ0Omp14lfG7SHwFqrTWn0zjDrz30kuFjTx1K98zsgyqjh2NBoZkL0B/DjudX2XrwiUMnQpZkYHk/8Ouvtx6oFYGiWEXvJjZlJpzJNBbugQHxTj6ZTDafY4ZIJILdu3fjPe95D+6991587nOfwz/+4z82qe7zzjvP9O9vvPFGDAwMNP+bnha05fQYqxWegmrPhGlNuK7VUVR45awO3ry+kQmMJkwU0lbak3RQcZYBHZ1SnoEcYH/Dj7/m48xtyVeBFFjtiThmjgxJnxJYHwJAjAwHAICcBYGME2iahrueoVR04/0pHZ0rK1xWt1Bnf/dxQd8zAMRJKUGRJFRqjb/NlGoo18g8Yot0tOuZcGGpIe6DBTqajO/MGXgtc3Q06QzotaHELGlPCmoaxsdPFz43GWB/86xBnRsAXljM4xcHjBma1WJNmLG6gUMW6sE6+mHYYVgP3v0ZoL304o8Ab/gz19+fYlMGYbeQSqXw5je/GQ899BB++MMfIp1OY35+Hv/yL/+CW2+9FWeffTZWV43rLJ/85CeRyWSa/83OGtcvewVq1BGQfIi3tRskBc3uRgrpilLnshV9EaJ14ZRZTVhk1KHDgmuWqmooBn/F3HdM/BV4w9Y3YIBkNL7QfE9qwnMauxhPEdvA5vsHwogSpYuZJWI32LeYx4spdqF9y6mNzcGWwQhCZMYzY9pRyWORDImfMJgYExVsLPSZwiIVrVEQ7vkkpbbNH6WjqTo6QbJ7IxW70fAGHb2mo2eIIHCbKkH2857lAPjhLIqxwvnrv2Sz4OEYP5HsqR5R0lQZvY0oo4u1Ir6777v4/v7vIxpir6VeTFISKqMXnwOe+jb7xLM/ACT4a8FtbMogrGfARtluNps1zJLb8fGPfxw///nP8Z3vfAeXXnopBgYGMDExgfe///347Gc/iwMHDuB//+//bfj3oVAIyWSS+a/foJnwsBxCO6EU0zTIpAfQqC5MFyCgIcwCwLUpMZkwN0dYLCQBYMk1az6Xhi/xFHPfbxz7W5AkiXO1kcNzyJRqUF2c0KPWypgnV8aUwNRCB2+J2Jua8F1EFT01EMZpWxvnuU+WsGOUrVszCunMLBb8bFCcHBW3ZdDRfwBQXMvuqShrNB5E0C9eRugkJddblNaU0XUAadKiRNXRceKRnTNgXbnugBhPR7fD7SA8m2GHhmz3G6t0k2RDm1XF9d5StY7vPMpqHN7+mm3YtW2Que/JHomzaM96ez24Vq/h/T95P679+bX4qwf+CnuUrzDPdTsTNpwh/LNPA+2dDcEEcO6fuvreRtiUQVivBYvqvqurq0ilUh3bkwDghz/8IYaHh7Fr1y7usTe96U0AgEcfNRcHrTeWyYI/TJyBZIBv6jcIwtQtyCdLzUVnlLRhNIc4qKrAN9oGHS3IhH+w/y5Icuvi0zQZv3P8WwEAJwydwDxXDs1B1dxtf1leegY1UhvbMs6fIzoS5DLKG7gxdYsfEyr6klMmmBoepaTbM+HC8l7kqVtWUvw7BcPD8Gvi7J7rETbIgoE+tCitZcIZWYZKfi+OjiY1+rIsoVZhWQVV1bBSMO4TBviapetBmEx32hbm2/eax8KNMxQfy/efOMJklJIEvPusY7BrKxvEnzqctnm01mDmlnXL07fgyaUnm7cPVu6D5G9tBtyuCe9d3cvMEPZJPhxXKgDP3cE+8Zw/AaLD6Ac2ZRC+4IILAAB33XUX95h+n/4cM1SrVWSzWVSrfAa4tNRYdEIh96fzuAnespJ/jlWFNBWlDEWDkNdEIhwdrWfChSWAKk1NhVmUjuZ333fN/IC5LRVPxNZkYxGlQdi3ppDOuCjOoj3CAU3DyBBvWakjLtGMz7xVxAkOp0scXahT0Tp2jtFMuBWEF1JsHQwAxg2EWZLPhzhhFgprQXg+w/7WRqIsoA8tSs05wnz72BAxUUkIa/fsWMd0qcb10NJMuNfWlbM19trcnjS+lpIRNkBnDSj2rxEq+vzjx7B9JIrTtrHX4pOHMj1xzuJ7hBuZ8IuZF/GlJ7/EPd+feKb5b7e/X26G8MAOhO/7HPuk8CDwuj9x9X3NsCmD8EUXXYSdO3fi9ttvx+OPP968P5fL4YYbboDf78dVV13VvD+VSmHPnj1IpdjJKeeeey4URcENN9zA3F+pVJr3XXjhhT37HG7ArD1JBxeEjXpzTUQp1JCgmQlTUZYcAASK4SY6CLMO5w/j+czjzH1x5XXNf1N7OTm4AshlpF0c4jC3wnrpTmoyZFncJwzoo/9ayFfcn2bzE0JFD0QCeO0OdqdOg/CBtvrxApmNnIQPEb+xQCZGs/s17QGtCRu5ZQF9aFEy6BFOBpMI+NjfJJHgBx7kic0jPf+B/rcozYB9vWkTO8VEjARhAcX+5KE0RzO/53WNctEuEoRzZQUvCexOu0GmVOPqutPDUaiaiut/cT1qApU6E4RdzoQ5u8rQKLDvx+yTzv0oEBl09X3NsCmDsN/vx8033wxVVfGGN7wBH/jAB/CJT3wCp59+Op555hlcd911OOGEVsZ000034eSTT8ZNN93EvM5nPvMZJBIJ/N3f/R3OPvtsfPzjH8ef/Mmf4JRTTsGPf/xjvPrVr8b73ve+fn88W+B9o/mFJEG298aWfcaiFKoSbWbCtD1pYCsgm5xWnDCLXSC+v//7zG2tHsaEv9WicdzgcfCRiThyaMHVNqU5YmoxZWBqoSNBRv/la+4HYUpFX3TyOAIk+FA6erZtkMNijrUVnTDoe9YRlyjFngYg6BE2o6N7XhO21p4EAKHQAEex5wrsd0rrwcmwn6t39zIIZ9IHkSXtSdsnzzR4NpAkiv2qJKFcSjP30bakLQNhvOmkBgMymQxzDJfb/cI0C5YkYMtgGP/xwn/g0QVxqc8XfRGSr7GBdLutjRNlLbC3ERsDzvqgq+/ZCZsyCAONDPWBBx7Aeeedh29961v4p3/6J4yMjOBrX/sarrnmGkuvccYZZ+DRRx/Fe9/7XszPz+Omm27Cbbfdhlgshuuvvx733XcfwmHjRWYjgAvCpM4FX9AyHZ2i9bA2Ko4Ks7JlpbHAW5kj3A4TYZamaVwQrmVPx1i8FVxCvhB2EKWyLzTnqmHHHDG1mAoOmj4/TjLKXM24VcQJVgtV/Oog+ztTKhoAJ8xSNTQzmwXS9zxB6FqKmESp5MbiTIc3mAZhkglX66pwupMjaFpTEEjHGIqCsCTLSFIBXZFlxqgwUeQU18sgPHvkYea2T9MwZdAjDADJJN9ils21BFiZYg13PMFOVnrnWdvhWwv0kiRx2fBTh9J2D9sUh0g9eDIZRq62is898jmDv2jMC/fFG0Ms3BRmCWcIz5EyzXkf76tlJbBJzTp0nHXWWfjRj37U8XnXXXcdrrvuOuFjxx9/PL7yla8IH9sM4IJwm280AGD765DMsjVOq8KsERM6GmhkDls5t6wOQdhEmPX40uOYybGvV0u/GqPb2Sz8hKET8EL6heZtXSHtFuYqabRLzLdETeh1AHF/FGjbvxhZIjrF3XsWUW9jM8IBGecfzwt2EuEAJpIhxkxi/2IeJ0wksFDNAm3q6AmDvmcdMTkItM0ezq/1TVt1ywL4IAwAhUqb53g3yC+2eoRJqcBoJF1ck9B+tVAV+3IHURYgcHRykS6dWWQ7AqZUCQEyVrIdCUGfdzY3h/HxxmSs7/76ENPT7ZclvPO1rBjvtK0DzEAHtxXSs4I5wv/zV/+TY+OmE9OYzbU29IHE01Ayr0GuoqCuas2NQzd4KfsSP0O42vb7JbYAr/mjrt/HLjZtJuyhgY414eMusuwfzfVIttXDBiIBbsJJKlcRtCfZzITb6OjvvfA95iG1Mgq1PM3V5ThxVmgOGRd7hefq7MIxRTYWtbqKa/7fU3j1DT/BB/71EYR95qP/ugUd2HD+8WOIBMWBbOcoUUinCkCthEWN/X4mTAQ/ABAnFHuxWkBFqXPniGkQDvNB2DVKum3z18moQ0eClDGogK5TexIADJDe2lxZYTZI3WCW+JVP+4wDMAAEAhGuRz2bb4jNNE3D13/JbmgvOXUC44S5oJnw04czrrb7UWV0aOB53HmQtQn+zR2/iT85gxVC+WL7ALkRMN06Z7gZworCzF7H+Z9oWOv2GV4Q3sTQNE0QhNsDrgTsfCNPRxv0sfJj3FqLkCRJ3KKUylfstScBhsKsslLGjw+yAola5tUA+PflxFnheawW+Fq4I6h1HCGmFlMk6N/1zAK+/ssZLBequOvZBRxMkVqj6t6GoFhVcN9elkoWUdE6jhsnCunFPJDme4THh8RGHTpihGLPK0UsZvnv2KxFKRLwgSYwuYpLmWO6Veu0UhMGeAFdtsJmfWZjDHWIxhm6NWRghqi1t4fFGX07KMWeXSs7PHRgBS8ssqzYe87m+/dPI21KhWqdEfR1C6YmLFWwr/5V5vFkMIm/eO1f4Pxt58Mvt85RSa7DH2sETbfYBq4e3J4FD24Hzvx9V97HLrwgvImRq+WgkBGCw+0TfKIjwMSpSIJdCbNEkKKDzwTYRYhTSGfLguENnYKwwDFL07B7djfytdaioWkSapmGKIUuhtSwQ5KrOFIk84wdIr/yAnIks5oig+8ffYnNoGaWiYjJwBLRCe7bu4RK2+B4nyzhopONfalpJrw/VQAyM1ggFPBEh7JB3M9mYQWlxCmjIwEfR8+2Q5Ik3rrStUzYfhCmAw/yhBHiyjExa0HYrVLIoWqaud0cKmCCJMnuc8XGBpu2Je0ci+Gc4/igPp4Mc3V9N/uF292yQmM/QaHO1uE/8ZpPYDQyimQwibOnzmYe8ycbKmm3vl/OrrK9NfWCvwQMnMl6DS8Ib2JQy0oAGGrPhOPjgC+ARJxtz8gJ+lg1TRPUxNhFiyqk8+lFgIqQ7NLRag1QyvjefpaKrhePg6YMrr0vOY7IKMIy+zoLZXYQulPMLTzJ3Tc5xk6xWSIZU01lA1ZeE/drOgH1ij57xzAGo8aLxXHjvGFHZfkAF6gmouZ2fLEgO3UoXy9zblmTA+GOhv+0TalQXT86Ou5ng02uxmaKnc5/oLHxoBPF3OplnSFWqdPDJxg8s4WkRLP7VSzmyvjx02wJ491nH2P4W4n6hd2ApmlNYZYcnkVg+EHm8ddOvhaXv+Ly5u2Lt1/MPO6P7wGkmiuZsKZp3OCGkyprQXjkeGDX73X9Hk7hBeFNDEpFR6UAIu1tGGtG/MkhVk2cJYsPABSrdc6Yn2YCNBjWV0kWLMlAku/HZEAzYQBLqy/i50d+ztxXS7dUobQmLEkSJsKsecZK7aD5+1oE7REeUYEQWbxTZJRgpU4CluROEK7VVfz0OX52sBl2EoV0rqxgZtG6UYeOOAnCBbUmcMvqbGTTs0lKTBC2lgknSFtWjgwy4Sco8ZsdSZJ6opAu5uaQIpuJ6Qnx4IZ2JEntPltJ41sPz0IhQr4rXrXN8DU45yyXgvBSvrK2ptQRnvouJKl1TEE5iL953d9AUhXgV18Gbr0MF/7iVkhtrJ0kV+GL7XNlk7NUWuJnCOt09IWfBHzrp1He1Orolzu4ejCpeWHNqi85ejJQaCmks4IGeaFvdNycjpaoKCu5FfDxdB0DmgkD+OGLP4Talj1q9SCUXIsCFi2G22LH4aXi483beW2Ge44TzGXYjHqLzAcamgmXuSAsQavXIQmcnOzglwdWOKODS041z2C3rg1yaKewDy0fYNTeEcnHmf9TxMjvlNdqttqTdFCFtGuGHWtBuCKBs+M0VEeTqUN5MvCAp6PFm4yBSIAJ2G4E4dkjv+Lu2zb12o5/l/RHgbZuh0w1h+//ir0u37prCycoawfNhJ85koVSV+H3dZej6crowPADTWc7HR/c9QEce/gJ4Ke/C6w0BGkjAF61ZQqPhlrHGkg840rNnVLRUVXFNkUBxk8FTvmdrl+/G3iZ8CYGF4RBFv14IwgnJljf44oEVIhJBh1hGPTL3AJKM+FQntRhO9WDgUbdpU30owH43uzdzFOU3GmA1gq8wwL6decA6w1ekQ9xz3GCOSKOmQzwwYp+V8U6u4jVJQmlElv7cgI6O/j0bQOYGjA3DpEFgxwWiR/xuD/ekUaOkT7igqbyc4Q7HEvjdXpgXdnmV74qcDIzrAmTjUWubeBBVVG5YErLL83X6UEmfGiRLYOMq0BEwBpxxxJgf+uFYhaH06y6X3fIMgIVZ5VqdXb4h0McWi1CCiwjNPZT5v5XxLbgvQ9/G/jWHzQDsI6L8yxL548/h3Spe9ElFWWdWK02gt+brjE3F+oDvCC8iWGujEaLjt7CN/zn5h5jbtMsYDQW5BZqOsQhXmaNADoqo3W0KaSfCwbwQoEN5rVM63iHogHhjvwkIs6CfxWZSvc02hHynW4htG1VUTl3rrw6yL0OtUS0C1XlZwdf0oGK1kHrwmmF1QBMkIlCIsRJNlmQVCxwmXBnOronk5QKi02/cmrU4Zf8hll+nPiW59sGHqwKWtxENWGgN4PnZ1ZfYG5Py9ZaZehnXa6wFPtpWwdw+vSg6WuMxEPYOshuqJ50wbRjZrmA8OR/MMNYJADX7nsMgUMPC//mogJx2PIXsTfzRNfHsmf5Web2idUasOVM4MRLu37tbuEF4U0MLggrZDFYo6MTiSnub7NHfs3ctiJKoa5ZQzUSaDqJsnS0ZSR3xNmAMRiYQL3YqmHTerCOU8ZeAU1js6Cnl54XPtcO5shg9Kk4W0uj3xMAFOqD3H15AwW6VTx5OMNlnm/pQEXrOK4tEw6ihrTEHvN4jD8fKGJRNlDnJQlLGTZLMesR1tGTSUod6sFGWX6cmzrU2rRSdkOWgEGBEhrojWvWbJ7d0G4PWZvgkwwNMrcLpB/83WdbuyY55ywX7Ct/ufRT+OPspLvfy+ZwRkXQwreW9U/V6zilwv4W+/I/559vE8/PP8LcPqlSBd701w0fzXWGF4Q3MbggXCUmEWsG7wE5gAj5qbNLzzC3aXuSKPiNJdj7JlUyvN4KHQ00M+EagP+Ms8riE+MXoP20NMpGxmIxqBXWNerJxeesvb8RVBVzYIPEFOmnTeXY78kvS7j8zGMRIgYHe+e6q1HT2cE7x2J4xXjC4NksdrZ5SE9Jy1gk2eLEgDk9CQDxKPvdlmQZxRx7vpn1COvoSYuSWRCOGAevJMnu2wV0lAkajrUmiFEMRNjP5EYQnqmw3+10nHfDEiEZYcsGJV/rMyXCfrztjA5CyTW4rZBeLa/imfK/MveNKwr+20qafeLQscAVtwIffw445lwAwMUFlk4/XPkloxmxi0JhCTNk7vpJwycDx13k+DXdhBeENzF4y0rihBVvLaRJH7tgZlfYHSrnliWoh9Ga8FaJBGGbmfD90QhWySK6xfcG8p7iTDgR9kOtsBndnpXuMuFabg5LXI/wKcztpTwdah/CX/zGSYiRIPzjJ5/vaiwcdcm65BRrVDTADnLYKqU4ow4rQTgW57PuINjzzUom3JMWpdWDzX9a8Y3WQTcWeUmCtmZkwzFBBqIsoDeZ8CGNPa+mhzrPQweAJCktFOXWOfdfXrUN0aA17e2urYPM7WfnsqjR8pZV1Gv43J0fhCKxrNI1y6uI69dEdAT4zc8C//Vh4JW/CwRjwLu+CWx5FS4qspR0GRk8NfuAs2MBsO+h/w2tLeP1aRpe8cZPbYgsGPCC8KYG7RPm6ei2IEzqYdn0DNBm7MGPMRSb1+vWlQkUMSCRsWdWg/Aa9XRHnBWVnDF2BmoVNlsxWgxlWUJQZbOFA5l9wudaxeLCk9xw+C1jpzG3aSY8mghiciDMjf6bSy8xnrx28MJinhPGWKWiAWBH20jDbdISZ9TRqT0JAGIChXFcbmVHssSXJ0ToSYuSg/YkAEjE2M9dlySU1uYkm/mmUyTDdKZwd0G4VlzBHMm6p8d3GTybHAuZk5yXAawNrbdKRQO8OKuqqNi7YHMamKYBz30fD33xLNyRYVmpiwtFvKlYaogy3/BnwEd/DZz9QdYgI5wE3vMdDIZ2YGeV/U7v/snHhbPHO6KSw55nv83ctUMKIbTzjfZfq0fwgvAmRkff6LYgnCA75qxWA1Za7Thcj6SAjpYkqRmct0oC9a9gqosQ4STSsox7o6wY5G2veBu3GTCqCQNAHOwic7jwIuqq8yk9R4h4I6IByfAgcx9tT9ID0QBpDwv4Cvgf//mco2yCZsETyRBO3zYofrIA8ZC/2T60RVpEigSqyQ4DKQAgSlS3ABD1tRbl0XjIUgtLPMR+L660KLUHYdlGEI4LtBFrXst8j7D1TLjbIHz4yK+4zd/0lrMs/W2SzO6uyDIiUgFn7xjG8RPWyhdAwxP7mBG2NGSrX3jmIeArb0H5W7+Pvw2ydHJcVfHnqTTKp70b+OhjwEV/I/QLAABEh/GL19+MVxfYc+unWh7a198OVG2qtn/5L9hDZjSfNPlqe6/RY3hBeJOirtaRrqSZ+xh1dDABBFpBLhllM5ucTwbmW6pDzrLSYBFqBWFCRccnrZufh5L4USwKpW3hCcpBvOXYt3CLoREdDQDDwWOZ2zWtwk1hsoN5Mvh+ixTgRD5LOTFjkCD90bKvhANLBW6eqxXc9SxRRZ8yaVifNMLOtWx40L/IfM+AtUzYJ/sQJWx6WG4F4SkLVDQAxEJskHSlRcmBWxYAxOL85iOfb3zXnG+0yebPbTp6ZoFV/w6qGpKxMYNns0gKascJebljW5IINBu2NFs4tQ/45ruBr7wFmP0l/mUwidkA+/38RiqBDyk3IvS7/19nMx8AocEp/DB9FXPfbCCAvfOPAd+8EqhZHJBSWgUe/Ec8TzaCJ20719rf9wleEN6kSFfS0MCukoxvdJy9iGkrQ1aWgblWb6LVRUg37NhGM2Gr7UkAEB7AHQk203rT9jchGUyaDpGgGA6PQFXY3T61prODI2Tw/aSfnytKM2G9bStOTD1kubFQ/O+f7kPaxoSn+UwZT8ymmfs6GXSIoNeFIwH2d/JDNg1U7YgTz/GQr6WOtiLKAnrQoqSqzOQuO3S03x/ipg7ljOhoG0GYGqrYxSyZcbtdYBBjBNFM4S3xQkdnNRH42cIdgvCL9wP/ch6w5wcAgOcDAdw2wK4zkdIYbl2+BpWhkzr2putIRgJYKJ8CucZe23fHosCB3cC3rwLqFjY+P78JSiWDfWRTQAfArDe8ILxJQaloABhsz4RJ/UsYhOcb80s1TbMkzAJamSlHR1utBwM4AAVPh9iF5m3HvQ2AvcVwMBKAWmYpxr3EdtIO5srsZ9oS5vtpqWWlTkfHydQhbW0MW6ZUwxfuZntAzUANOpJhP163s/M0HQo9E5b87OzosWASPoHBhQgxYv4SkFsaACuiLICno7tuUcovAPXWOUKFWUZuWToSJLvPrZmqpGzQ0SKzjm5EeLM51mhmW3DI4Jk8qnU/ImRjce6OhtmOXZxGxFl75rOoKCblnV/c1JzpXAdw/egw6m2BVtN8SB15DwAZ08OdjV10JCN+ABLKWda286extdfY+yPg/32Q0bRwKKSAh/4ZLwX8qBAzDjoAZr3hBeFNChqEB+QgmKUhxgYQGoRzsgzMPwloGrIlhfGaBRzQ0VbbkwB8r3CQfU1NwjlbzkFFqXOLtJlAZjAagFphd/zdZMJzNVaIMhXnqTPaT9rMhMnUIdXXWtT/9RcHcWCJ9+sWgRp0XHTyBAIO7AOPG4vDDwU1PyueG7dg1KGDjv7zya1an9VMmPYJFypKVwGrnYrWYC8TBviZwrk1caOVMYY6aCZcVzUUqs61CLQ9aXvMWlsRAHzv8SOcMv+kCWcbnVduZdeIWl3D8/Mm4qyVVvnmm8k4ngqza0Y1dQHUaoPF2TZkPhu5Hbrwrd26FgD2BYOY0ZX+T38H+MGfNsRgIjzwv4BaAXuC7O84EZ3AUNj6Jqcf8ILwJgVvWUlaEeIkEw4JMuHCEpCbR0pgQNErOrqu1vGDNNuj/FsVDX7ZL/avNmkVGYwEUCeZMLWnswxNwxwxOpga3Mk9jdaE9Uw4EWSp63qbS5Ciavj0f/JDFCgyxRoeOsDOer7kFPtUNNDIhCelVSyRjGgiYWzkTxGjFLuvFYSt+EYDfBBWtYYtomO0BeGcLHH17s5BmHpZN/pH6blnpkWgmTDQXV14ts4KmaaHjrP0d5qm4WsPvYRInSzjWlb8Bx2QCAeaDIoO037htXr6vM+HLwwNMg8F1AlUly9s3p4eth6E9RJGvbQdqsJeV3fH2jLqx/4V+PFf8YE4Owc8fDMAcEH4pOGTLB9Hv+AF4U0KLghrpN5ChB0JMhUnq1M0809xFHA85Ec4IKYsDdXRg9aEIL+c+yUWa+wi8bZ8Q/FIj8Mn8xNr2jEQDXK9wgvFBUf2lVphGXMk49wywl6wFaXO1f90A5M4YRqkIKuK/ulzC/j5C+Z+0nfvWWAYiZBfxgUnWhPoUGwZiGCnn+8RHrcThP1kYIfc2oBYpqMF84a7qgunDzb/SZXRADpmOTS7z1WyKFYVFEkma7b5S4T8XIupU4V0vZzFIfIxtpO2OCM8PpvGs3NZhFX2BbKCUaVWYXmiUq0MlDPQAPzd6DCKhPKVUlcAWuu7nh6yTkfHgn40dIgylBzbp//TGFHtP/RPwM8+zd53/+ebNPme0MauBwNeEN60WC6xGZNZexJgQEcDwPwTWClYbwsajYcQQRmjEtltW6Sj6dzgkytVHJ9PA5rGUb1mrkXAWk24MgaNLEJ7V+3XhdOpZ1EmC8nUOOkRzvOZ+li8EYzixD6w5tM4NuGGHz6HumpMxVIq+g3Hj1k2W6CQZQmnJ/JYpO1JMeuCnRih2DUHQZiqo4Eu68ImPcJRfxQRv/linyCmNblajtv8AeZ0tCxLnAmJ00x4Ye5RLpu3Mj0JAL72UOO7CNTZY8l24aF+GmmFM1RIFxo98D+JRrhWw98+7newvMyuB3YyYVmWkDCgpJ8MBbHgJxvz+z4LPPh/Gv9efQl49DYAjXLF814m7KFXWCU2bMM1Qil3CMJZPeube1LQnmS8AI0lQtgiLfMPWKCj89U87pm5h7nvbfkCoNWBaoEXh5lsBoBGTRjwNetOOpxQ0keWnmZu+zQNY6SvlIqygj55TUQCJEgGlkcdH7+EHcr+3FwW//4oGf+4hnKtjnv3snV2OwYdIpwUWeWMOiai1l8zTubvqm0Uu1U6OuT3IUgYhq7alBy2J+lIkCCdqxW5tjjRBDEKOhrQaRCeWXicuR1VNYwkO7MV6WIVP3iy4TftU9nrJFt1RkcDvEJ670IOZVH5ILeArCzhxhH2Ox8Jj+CKHR/inm4nCANoXlf1wk5odfZcu+ec9wJEuY+f/E2Dgr7vs8DaqNZFn49z5DtpyAvCHlwC55ZFpqfQmjClo/OyjDogpKPNqLixeIirB9cjww3buQ6466W7UK63evz8moZL16hoVLK2XIsAPQgDarl7cdb8KjtSbRx++GV2IeZ7hFuTpmLEszgPDb/3mmmcSAwT/v7He4WGFfftXWJqpbLUEGV1g+2+FBbIImSlR1hHjNS5Fblx3ImQn/OENgOlpLujo535RutIcDOFS8L2vE7tNG71Cs+SDeO01Pm9AeDfHz3UnBkt19nrNasURX9iCadMJdFOPtVVDc/OCYJ6fgG3DSSRIpu8vzzrL7GaZ3/voWig46aGouVK5oeSP5l57G5lFfit/8X/0Q//DHj89ubN54PsbxQLxLA1YdFQqI/wgvAmBT+8gRV3dGpRAtaGoa++iHyWzWzNRSl+HONjg3AlZu3E/t4LLBV9XrGE4TXvXpSznEDMbDMAAAORxnHWK92Ls47k2Ax1ys9vKoyU0QCQIFOHcrIEv6ThmsvYBSSVr+Cfd/MtS9Sg46wdw6ZlASuIqQscxT4Rs5EJk3NGkRubhAmLVHTzddyapNQ2Rxiw5xvdPBYShLP1su3NH+CedeVsljWX2R7sPENYVTV8/ZdtKvE6m91nlRL9E8uIhfyM9zhgUBfOL+CXYfY8eMPWN+Atx74Fh1bYTYDdLBhgv18ldyrz2CMLj2D1lZcDl/wd/4dtgx72RNhr+MShEyFLGy/kbbwj8mAJnS0rSYtSiA/CujgrssIqd80WIUmS8IogS4Xnwp1bKmZzs3hskZ1h/Nt6Fgx0mQmzQXh/ej8U1d5CP1dkfZ6nQrzAx8gtCwDiZNNTkyRUiks4/4QxXEjEVV++/0UcWm0tVEpdxd3PsUHYidkCRUnhxykm/dZ7juPEsrOyNqHHKhXdfB23Jinl55tUI8BnwiPhzp8tQWr3ebUmsGztbJbhlnXlbJndAE9HO4+Z/Pn+ZbyYal07dZUNNlnVujmMCJYmKuUXsUiy4CtOuAKSJGF2laq9HQThtklVSv4E+KTWWlDX6tg9uxt4/dXAGz9p+Bp7Jthy0EYUZQFeEN604IKw2qbG9QU5b9awL8zRq3oQHs6yZuvDHRahY/zswrEa6Jxd/WD/D5jbA6qG84ttF2s5I2gT6ZQJNxZCmglX1Speytqzi5yrsgvNFsHMXZoJjzFBmA+auVzDeOOay06Gr43jqyoqPntnK1v/1cEVrBbZRfzNDluTmlDrWKmyv5NPCeNw2voCHSVBuCw1RGVWe4R1cL3CTicppdmscYUIdCzVhMl1kdcUWz3COtyio2fqrBfytKAtjoJaocbJhjGrdWejySmkD6e552i5Oc6TXC91zJJMeJsNow4dDNOgBTEZOIN5/O6Zuxv/uOC/A+d8hH+BUBLPEwZ8I4qyAC8Ib0pU6hXka6z5A5MJx8a4MV2SJAlcsxrPmSqx04fM6GgA2ApWQLQgmdcZNU3DHfvvYO77TcUP5l3KGVvDGwAg4FsT0NRjUGvsZ7NLSc+prB/tZJJvuaICttG2+coJAc2bX8uuXzGewHvIRJs7njiCx2YajAJVRb9ya9KWuYEQuXkskqtbVQawf9G6AX6cGHuUZAkhVDE5YN1WEXBxktIqG3xWguzi3sktCwAS5Dk5qAK/cvuZsJMgrFWLmJVZtfz2sVcaPLuB+UwZP3mOni/suZqF89m7AK+QfmExz4npMvk5TtU9una+zK4SOtpRJsx+vyNghy78/MjPUagVGuvcJX8HvPq9zOOFc/4EM3nWhtYLwh5cw6qgD3CEsawU95YKrSsBHFNjRUmd6LixOkvdHoK5C9Nji4/hUJ615vtteZB9UiXLq7Qt1ET1xZD2C9sSZ5UzmPOREYYjPHVlZNQBAKFABAFiGlAotmrnf3rxCUiSYHTDD56Fqmq4i0xNeouN2cGGSM9wdGGtNmzZuQsAYnT+riwhgRImB+xlNhwd7bQm7EImTDcWOYlnOKycdzRIOPGPXl54AiVSs5+eeo3p33zz4RmmzS0S8OHsV7DmHjkJxk5SFnDKVJJhblQNnDhrqciXOvRywOwKoaMd1ISp53i49kqGyaupNdx/+P7GDUkCLvsH4NLPATsvBN70Kew9+S3M3/slP44btGaC0m94QXgTglLRfkhIqA6C8JqwZac2iwBai4gpHadUMKCwwqyDinkGQrPgnQM7cWqQLJjlLD9Y3UZGwjln2QjC5eX9XH1xapzPSMyEWQCQIIYpubYgPBQL4qMXsYPafz2Txmfu3IMjGTYLv8SFejAys5xRh6oM4EDKRiZMzqOCLCMuFWzXhKmS2nFNOE0yYYkMMLEQhOn83ZIsYTXHWjNaEcSJ/KPtYnae1UgENQ0TQ+Z09HceYzezl5+5BRNDbEtTSZZRKzk37IgEfTh+nBVn0bpwinRnDPljCPgCyJZr3Hdhx6hDBxW+FctBnD11NnPf3S/d3bohy8BZ7wf+4D+A8z+BPeT63zG4AyGfPQanX/CC8CYEDcKDcpD9IeNiejgRYttldMOOoFTHCVLr4jYNwplD3F37ysYuRSWlhB8f/DFz39uOexskUpurFdMo11garRMtDrSJs0gmbGeQw9ziU9x9UwI62iwTBoAY6V3Mk9/pD845FseSma1fuo8dn3jsSBQnTPDTm2wj/RLmycZCqyWx30YmHCdBTZEkxKWc7SBMsxrHfcJtmXANQJrUPi1lwjH+2iiXWCaiX3T0zDIriNyKgKl6t1Stc1nmO14zLZyklMmK+9Gtgp+olG7d0DSkiIZiZK0uTevBkgRsdRKEOaahhou2X8Tcd9+h+1Cp85a7AF+O2oj9wTq8ILwJwftGk5/RJh0NAKfIB5v/HoqaBWH24s5qUbxUNLaWfHj+4UbtZg0SJFy28zIgzB5LOcfv3K1kJEYK6aXSknDSlAhzxGFrQJMQDbDBslzjh0vQTDgu0dpnmrkd9Mv45KVsyxLFW06dtDzyzRQCOlpVBnBgqWB5gEJM0Psd9WUwYbcm7FaLUlsQTguGWlgKwgleyV+rsOWVfgmzZoh4cHuA72Box2KOn6P7ivE4BgQDH7L5OdvH0w5T56zSKpZILXtsrXRBNwkTiTBC5Dy0Alq6yZZruHD6QkhtG92iUsRDRx4S/v0e0vGxUZXRgBeENyU4o446WVSdBGGpsSAMRgPmU3tIXe6wNso5SbXjEBnTdtroaQ3rRNIyVSummdtWXIuAVq+wWh2BprLPt2pfOZdhF8MtPn7nTrNgoDXMQkdCZhfvfJVv7bjklAm8bqdxsHCFigaA9Cxn1KHVkshXFCya/F7tiAX4IBz35TFqoYWH+Rs36Gi1zrAwtHwgQcIgaT8SIRIahJ9sQoIgWZ2FTJgLEk7o6BIb/Kc7uJnR3y0S8CEe8iMQCHHjDLMFNru3C6qQPrBUQK689hnzi5wyemxt4tghKspyoIwG+Ew4V1YwGhnFmeNnMvf/dOan3N8qqoJ9q6zYdKOKsgAvCG9KcJmwQhYAAzra0D8awClyIxB1FKWk2Uz4kDaGXEURW9uhkZG2o+ldTOjoepFdCEctuBYBrUwY8EGtOLOvPEIWrEmBYQKtBwf9MucfHPfRIMxTv5Ik4VO/dQo3AABoBPUzpwctHXMnlNIvIUuDsNL4XFYp6aAchJ/s74YjRVM/bxFcaVHKsT3Cy2R4w1B4yNKcZEmWESefKUJmLtsRBOqoKKrhNWCEWYW0Jw0ca/r8xSx7Do4nQ81rJEFKIdkCGTVqEydNJRAgYsWnD699T/kFLgiPxMTtSU6U0YDYDEXTNFx8zMXM/T+b/RnnCXAwcxBV0iu90WYIt8MLwpsQy6TBf7hKaKqYWK3cKROWoHbOAkgmfEhrvJcoUwSApSK7GOi0FQ3CqJCF0EI2AjSGOOig/cJWM+H5apq5vUWQkYjqwXSTECcZdK4mDnanbhnA21/N+wO/+ZQJ2wFOCFXFoiATUptB2Jo4S5IkRDV2iUiGeUq0E1yxraTK6CB7flihonVQAV1QbgmzzCaItUM03ctWNqxUMCuxQXt69FSDJzdA6ejxNiYmCTJJqWQ+sasTQn4fTpxkNSTNfuH8ApZoJhxZo6OJUcc2B8pogDXrABoK7UK1ztWFM5UMHl14lLlvzypLRU/GJjFIet43ErwgvAlBM+GRCllUBeITQDDOsI12TkglbJcWO2cBGZoJN4IwzRR1pMhioPcSUjpaIkHYqmXjYJuRPq0LW86E6+zufSqxnXsO3yPMbxISpI5cMLEP/MQlJyIaZBey33CLii4sYoEs8KgHAbVxzHbalMJkiYgEHARhN2rCVBkdYxX5doJwXGK/94Cvdf1YPe+6nSmcWXwGGRLItk+92uDZDVA6ejzREsglZSpkcq6O1nHa1kHmdlMhLciEm0GYy4TdoaOBxiZnS3wLThkh4w1fYinpzSTKArwgvClB+4Q7jTHUQa0rcz72RD9FeqmzKIXQ0Ye1xnuJxvwBPB2tX6xUmOWvsW0iVsQxQKsmDPAK6f2Z/aipHRbGagFzpNVlavh47ml8JswfXzxA1OcGyk0AGE+G8enfOa1pln/RSeN4w/Hm/daWIagH15XB5r+tZsIAECR19oDPvi9xTzLhCHv+2AnCNGD55VbgsHreBXwyt4nKlq0H4UNzbPYmaxq2dBAPUTq6XZOQJCMauxlnqINTSB9uC8JEbDUSGYGmaThELSsdZsLxoGBm89r3e/F2lpK+Z+YeqO2e0ZtIlAV4QXhTgmbCQ+09wpCAqLhvl6OjSR/pqfJBc6OOugJkWReawy7R0SGFDcJW2kQANhOuk2lKiqrgxcyLpn9fXz3IjfubGuNpQc6yUpQJ00lVHTx8Lz9zKx78yzfh+x85Dzf/4WvcUUUDQPolrkdYq7W+bzuZcIAEYUnuPhMu1eqmc5WFoJlwkA06tjJhmf3tpLaNhRXfaB3dKKRnUs8yt6fgR8DHZ3/t4OjoZFsQJiMaswalEDs4jYizXlouIlOsoZSbawx/acNYZAypfJWZBAY4D8KyLHHnTbbU2LxddAxLSS+WFvFUqtFmqGkanwlvYFEW4AXhTQdN08yHN0SHAZ9YVczR0dDQvhSeKh00783NHWnM/m2DGR1dq9e4ucfNTJhk5SG1CKnNbs+KOAZggzDUKNQau3B0oqRTS89y9ntTgzv451GjDsEmIRaivsSdF+WpgQhO2zbgXgAGgMwsFjlRVuv7PpwuWRYRSSobGFSp+yAMOHDNopkwHWNopybsJ33Ocuu3tdKbrqObIDybPcjcnvZ37g2nG12GjqbToWrW2Q4jnDCRQNDPhoinDmeQyh/hnjsWHePsKgM+yXZPeTuMJlXtHNiJnQOsqYnuJb1QXODWHC8T9uAqikqRa1BnfaONfZxpJlyHhmLb4n+K/JK5IIoshEUthFU0ArsoCFMBGWBMR8vQEENrgbdam6MLIa0LdxJnzS2zwyuCmngaD0dHCzLheJg1LclpKvecviA9w2X37ZsTTQMzhccMdYX9fmuw1t7UDkpHAy4EYeKPbGWWcPN4yJhKzddiLKzS0YDAUKJk/TPNENvH7ZHOc55pTXiiPROmG+y683GGOoJ+GSdPsdfpk4fTSBVZnUdEDiDqj3L14C2DEcb+0i5Ehh06qEDr7pfuFmbB8UAcW+Mbb4ZwO7wgvMlAe4QB4hsdF9eDAfE4w/Y2pQkpjQnZpJbEtSeNAmutESI6mlLRATmAAT1bFBxLAq2FwzIdHWEXTbuzhecyB5nbUzKvegasZcJ0OEBeskm5uoX0LBeEkwH22Ky0KeXKNdQV9nNWNPtBOBbkg7At1yzSIwwAKyrZiNqpCZOsUZFbi7sdOppmarYyYVJ+6dSeVFVUbsoYkwnTSUpdjjPUwU1UOpTBEsk0R4MNJset9iQdtBe7ffAHpaRncjPYl97H1YNPGDphQ84QbsfGPjoPHGh2GZZ8iLSbDxiIsoDGrlAi/YQLMksX0YlKDDJUlNUSEokyYSrKGo2MtgIcsdAEgKTUys6sZiThgMxQZnYz4SPEWWgqwB8XYDETpgMPJAD17sbKOUJ6hqOjt8TZ7+WABXHWQraMusqeHyUHY/J8ssSJmGxNUsrNAaQXdIXUPK3MEtYRJ4xQTbbom07gmI5WqpgFqZ2OmNctRdcX06JEmICs5tCVjIDOFn52NoUUybLH9OlJ3OAGZ8poHTzT0Pp+Txk+BVNk3OjdL93NecZv9How4AXhTQfestLPhlUTOlqWZMSDbBbwjMT2xA5m2Z0kAyKOYYMwv/M2FGUBgOzjsuEE2lWq1jISSZJMe4WXy8tcm1Q75simZkpACxarCgpVdtEUZsJR9m/LXRrpO4KmoZaZ5VpIdgzSINw5E57PVFBXSduVw8W9q0lKtAwSiKBUZ2vTtmrCRBRY9bV+234Is4rL+7BEmIrpyVeZ/s1Clv28QZ/M6CGSdDpUl+MMdVCFdDUjUEavDcXgRhg6FGXp4GrCbXS0JEkcJf3TmZ9ymbAXhD24DtqeNESMB4yMOnTQuvAeMgs4knrG+I8Fblk6hHS0UXuSDhqEpXaVqvWMpH0x0qojCBD1q9kwhzniWjSV4OtHqRy/wRAJeOJx3uSjIBCx9BTFZSyrFWiEUj9pfJq5baVNaT5bRrXO1k8LmuJoTF5XbUp0jvAgb3RiLwiz1G1JbhMEdpEJWzXrODT3CHffttFTBM9sgdaDxxJs2SRJNt9ZCYDafSB+xVgc4UArTIxJad6oY8272o05wu2ghh205k7ds/au7sVsjl2jvCDswXWYKqMBQ8tKHTQI75fZBUla4CcKNSHwjdaRF1hXGhp16AiLM+FY0GfJtUgHWxeWMRJgJyAZjjWslTEnsRf2lGDm6BKhAsMBsa81paMBIJdf5O7rKdIzmCeZSlAO4pUTrMn/gaV8x0EOC9kyKirLnORlCagVDf7CGJx1ZReZ8MoA24oWlINCn2sj0Np9qW0VtCfMYj+T1Ux4lrQnjWsyNzCEQhSEmWMh5YaiLKMm0I/Yhd8n49QtrWxYHITHodRVHEmz2Xq3mXDCJBMGgDPGzjDdfG3kGcLt8ILwJgMXhGskAzWpCQN8ED4kkRro8n6gIqAqVZXrEW7PhAE+G7abCSelxuJulYrWMRBlL9YBn8UgnD2MOdJPu0WQkdDPNSqwrASASCAKHwlsefId9ByCevB4dBzHkfmwhWodC1lzkdV8poxKnfydJAPlrMFfGKMr1ywahKPsxnEkMmKrxYtulgqyBKzRt8NmE8QInNLRsxl2fOU2X+cNxFLW2LISAJICBieXO8zd5wTt/cJjUgbL1Dc6PIK5TJnr/XbqlqVDNEmpHT7Zhzdtf5Ph3+8c3Imgz/rvuV7wgvAmA+8bTbISk5owwCukl+QwFMYfWAMWnub/ML8A1FladtHHvhfNGGlNeJzUTGkmnIQehO1dOINkMYyCpV6NxFm51POc6cDU0Cu451kx6gAadaoYKQ/ki3ybVk+RmeWMOiZiE5hMhjlxVKe68Hy2jJLKbtIKssT5fFtBV5OUqFFHhD0mO1Q0ACRibNlAkSREpTyGogH4zSaIETilo2cLrBhwO92cCsBZViZpJsxbnmZdCsLtdeFxCDJhQY9wNOiz3GZoBCstYNQ9qx2bgYoGvCC86cD5RtfoBCV7mXDdV8ULGtlFzwsoaZKNwBeERAI+HWkoUkczIAKZhJ4J27x4B0km7FNY6vXF9Iuo1vm67hFCC0paI2BRWGlP0pEgl1TO4kxj1yDoER6PjkOWJewYZTOuTm1K85kyFFITzssyULZvicgLs2yorGkmHHA+vAEAEoKAFfet2mdguD5WaxuLmSq7iZkWeJVTmPlGA0DIH0aIsDDZAtuL7BTtQXhEWsUK2aiMRcZwiCqjh6JdG9CYCbN0nDV5FhIGHQ0beXJSO7wgvMnA0dGqNd9oHdQ1S/KV8KzG0reYe4L/Q9KehIFpjJCFoF0hXVfr3LGO0ZqpgTrajkIVAAYJhahWiH2lpuAAoQABYD7N3jcq+YX0lZX2JB10OEDeBSN9WxDQ0ZPRxvdx3BhLLXcSZ81ny82hDzpKsox6KW37sDhhVsXi2D+BVeoyMYCwG4TjpH4KADFfxnbmRjO1fEWBUu8ghqormJXYYLK9Q3sSYD5BqXk8hIXJFt0phewYjSO2xqJE/Kuc6G8kMiJQRndHRQMiYRYfhAO+AC6YvkD4914m7KEn4Ic3tF30wQQQMD/5aSYsySU8o5IgPP8k/4eEEsTgNBeM2oPVSnmFMVUHLAiz1tTRdulompHkSwHOJUdk2nEkxxpATBlYB9rJhOMye+w5B9RtVxAYdehlgJ1j1jPhWl1FKl+BpvK2g4WifbGZ4xYlQY/wMumxteOWBQB+fwgRUr+MyBlblpWAwTjDDtlwbfUA5sgmaXrijI7vJZolTJEkG8BsyZ1SiE+WcOpaXdjnZ1kQHyQMh4c5o45tXSqjAT4TzpUVoZjQiJLe6HaVOrwgvImgairfosRYVnaewkODMHwlPKsdy963+BxvMkHakzC4nQtG7cGKUtE+ycdnLEaZsE1akNLR6WIVJwydwNwnEmfNkWOcMjB8sJMJJ3zsYwUXjPQtQ9MadLSPrwkDwE6SCZsZdizlKtA0QFP5z1pwUOfmW5Qs0tF08xeIYoX4Itsx6tBBCcyQP2ebgREF4U7irMNzj0IlmeS2sVea/k1d1biNIKWjASApsZuIrAvqaB1N5yw/MUkJJCBLMjdHuFtlNMB/v4qqcQMiAOD1W1+PMJkiNRWbarnzbXB4QXgTIVvJok4GKDCZcIf2JMCAjqaZcL0KLJGgxdHR5kGYtieNREZ4+zgqzFqrCXebkWRKNW4XLOoVniPjE7fEt3DPAXgjEtEYQx1xshjk+xmEy2mo1RwWSSY8EW0E4eNIJnw4XUKpKqaF53U1rsp/1ryDDItvUbJIR1MtwuAxWKmQkoxNOhoAEqBtXHnbDEzILyNI6qOdxFmzS6zocUCTMBA2DxbLhQro0ClhJkw2gNmqeyxMwzlLg+Jng+3IWs+1W3OE20EzYUAszor4Izh367nMfZslCwa8ILypQGusAB3e0FllSdXRklxGBvHmNKQmqDiLWwzN6ehFQlly7UkAEB5kbuqZsN3aHPWPThdrOGGQz4QZKqtew5zGBtfJAX56EiBuUTJCnPSr5pTujfQtIz2DVVlGjWRaOh1NhVmA8SCHhYxeg5QRVNnXK1TStg/NcYsSd95t5/zTnQRhWrv3+wq2GRhJkri6cKdMeCa9n7m93dc5Y6RUtCyJdRNJP/ta2WqOe45T7No2iARKSJP2+LHoGMq1OicccyMTFg3+MJrZ/O6T381Y8v72cb/t6D1/9NQcvvvYIfz8hRT2L+UtTxvrBuKZdx42JGh7UkLygwk/VoIwrQmvzVJ9Vj0G23xt2ev8kwDe1fi3ponpaMk6HS0MwpxjllNhFk9bTcfZVqN0JY2l0lKrTSp7BHMkY9wyygs5ChWFo8BMhVkkCOeJvWJPkZ7lsmBZkpu1+GjQj62DERxOtzYGB1J5nLKFH6Yxl2kdd1CVUZVb30HBjRYlq+poEoTVgWmskvq+o0xYDgJtPtg+uYRRBy01AxE/c953CsKHSHvSNgtUumgTKJpOlAzE0T7kKquYC+/s4JjhKI4N5/n2pPhWHFrlN5puBGHf2kzhdv2AEdPw2snX4n+98X/hZ7M/w9lTZ3OWllbxT7v346nDrbr3p3/nNFx5dmf1ejfwgvAmAu8bTYgMC0GYo6PlGiApeEY9Fpf4Hm09MNcmziouAzSjG5jGmEqDcCuzpOPORqOCejXnmNV4D9t0dJSnraLyGKL+KIpKiyZ7fuX5ZhCurRzgFpSpoeO51xHZcZpmwuT7zbk0zcYSBPXg0fAo/HLrvp1jMSYI7180yITbzCECqh9oE0PlHWRYjm0rSRDOJCegLpMxhk6CsC8MtAcpX9lRX6tdw46ZappZdbcnpg2fq4P6RouoaEA0ztC9DaAsSzhrtIplmfeNpsrooWhA6CjnBMkwCcImWoKLjrmIm65kF/Pku54csJcQOIFHR28i8O1JpFBkoSbMCbPQUEjvlQkVO/9UyyOYimMkH5CY4oJlvqI0a4zOMuESZKgYsrkYJkJ+LjPIluo4ngTVdnHWfOpZrtViKsHXhKkgJhr0IWaywCRCg8ztvGrDlKJbZPhMmPY90zalAylxzbp9MZLrpJ5bcxCEHdeEiVFHdJB7ipMgHPORmqVcsU1HA+YzbzmodcySEsg0ERCK0KlHuHkspLyTFfTGd4PTBit8JhwZwyFaD3YhC9bRzcxmu9A7AtoxkRR/127CC8KbCFx7kkJOSAd0NNCgpOcjJAusZFoLIKWiB7YCPj9GBbSsfhJTYRbXIwxwmTAAbAnXELDhWgQ0anNCcdaQsThrbpUd2RiDLGz6t9OeBADxCGupmEfva0pNCHyjdVGWDqttSvNtdLRMxFl5F7yjq3UVFaXDd1NXgAzbI7wSYo8/EUwg4OOZkE4Iy2wQrvuqthkYwF4mXM/M4BD5fbZbaU+y0CMMAElCbbs1zlDH8dEiN51rNDLKK6NdaE/SYcWwwy3oHQHtmPSCsId20Ex4qEroJgtBOOALIOInWYCvBCW+FSABpElJU3HMQKNGkgj5EfKzp5BuXWlNmMWrQqdjzi4yal0pVEi32VfOZdmNxZRP7PBjpz0JAOJkIczD/sQhx0jPYEHgG90OLhNeKgh7LxkKlJQdCop9mlMksulISeeOAKQbYJm4ZTlpTwKAkMwG87pcE6pxO8GOdeXi3K850dz0+Gkd34PrETYKwqTkk3VpnKGObf4sUmSDrCkJvkfYBaMOHdSww9YcapugVHTQJ3dtvWkFXhDeRODoaBqELdDRgKguXMZIIgRMkgVBV0jT9qTBRhCWJInLDJdyFaiaimXSxiIMwsE4VHIKbgs7u8hoXThdrHG9wgezB1GpNxa0IyV2kzBFaGQdS6Q9qVO2lCALYV6WAMV8UIJrSM90pKNpJlys1rnFR9M05j7aK5yv2/88ohphR0p6lfYIx7BC6FwnVDQAyGCztapPhSwQO3WCnUx4ZpE1wYlowAg1sBGAm6BkkJ0lyW+dlQFQR71uoCygQrzWF1eDro8wbAeXCVv053aChQxfe+/WetMKvCC8iUADG29Z2fmCBsQK6ZFYCJjcxT5Rd87ilNEtMQmlpFP5CtKVNBRChXFuWQAgSaiSCTKTYWcBi2bC6VKVqwnXtTpeSL8AAJgnbTZbYryVIeAgEyYLYUGWUS/1wbqynAXKaU6YRTNh8SAHVpyVLSko11pZVL3OLqoFB2KzSMAHGuNynRTSlIEZOobfiDoMwtSuo139bQd8kDDeRM6uvsDcnpYjlhZ5eg4aZsLEE7sgy1BcHCCynJ/n7ntpyYdZ6hvdy5pwD+loTpTVByoa8ILwpgI3vKHdqEMOcH23RhAG4XgQmDqdfaKeCXN0dCsIj1HDjlyVm54kQcJIREwblggtOB5wGISJf3SmWEMsEMM0UZ/uXdkLqHUcUdn3mUoSw5I12K4JCwZAFFwy0jfFGlthZNShQ5KkjnXhuSy7qCoqCcKaYntgvCRJ9icpiXqEXQrCCpmTXJSdlQ1sZcJ5tr69PdT52DVNsx6EE9u4+9waZwjwOg9/3Y9f7s9yn9kNow4d3DjDHgqzeGW0F4Q9EHALEDXqsEidiPyjR2JBno7OHgYKy4Z0NACMJdjgt5QvcxfrcHiYaZNpR15iF/hRh0GYLobpYmNhoOKs51efB3LzmCe1rakRscOOHaMOAIhH+c1GPt+HIJyeRV6SUCB0IQ3CgLgu3I55Qsv5fOz5kpcloGrfCYwOae/oH20lCNv0jdZRrrOfqeBwJbRj1nGoyjIi08TfXIR0sYYqGQoxbkhH8+WobP5Ix/ewiiXCHvmUKJ44xHpJSxKw1cUgTM+ZXmbClI72MmEPDGpqjbOhYy0rO4uydHCuWb5Soz1j5HjAT068g/fx82Pb6WhBJsyJskTK6DVkNTYID/ucOUxx/tGlBmV6wjBbF967uhdaeoY36jCwubM6S1hHLBCDRIROOQcDD2xDUA8GBDOcAewcpdOU2IBK+1LDwUHmdkGWHI0zjIXIhCk3grDDTDhXo5mwDKVm/9yznAmrKmZU9nudFvSlU9B6MMCzTzrC/jCCdJyhgEJ2hLqClEJU8QrfTTCRCCMkOA+dwsokJbfgZcIeTJEup7n72EzYmigL4IVZ0Olonx8YP4V9bM8PyV9LQLJFe9GglMpXuExYWA9eQ0Zld82DsjODAcuZ8MrzWE7t4QQmk4LxdiIqsFMmLEsyYmAZCSdey7aRmcE8qQcPhgYRppsq8OIsPhNmP3MsQsVmMr8xswDbk5R6GIRXK3x7XMFBwOLVuzWotH8fgJY9ghmuPWkX9zwK2p40FA0g6Ddetns1zhCFJU4ZXVME3Q0uKqMBUYtS7+joBaJC70ePMLDJg/DDDz+MSy+9FENDQ4jFYjjrrLNw++23236dXC6Ha6+9Fq985SsRjUYxODiIV73qVbj++ut7cNTOQBcfCcBAe13OQnuSDtoP26SjAWCKLAx77yJ/PAX4WxQ0p47OV6wZdaxhuc6e6HHY70EF+ExYz0ioQjpbzeKJxceY+/wGx5ivKKgohArskAkDQJxcVnkXp9kYIj1jOMKQgtLRh9MlFKutxY1mBCMxdrEtSHJDCGYTcUpHmy2ogjnCIt9opy1Ki2U+i8sV7AdhuvlTNSBf5T/X8sITKJGN3/T46dzzKGh7UqfAkJRo5ujSBjC/gCVyfpUVfgPkpjIaEJl19CYT1jQNcxmWCfEy4Q7YvXs3zjvvPNx///244oor8OEPfxipVArvfve78elPf9ry68zMzODMM8/EDTfcgC1btuDqq6/GVVddhS1btuA73/lODz+BPVDf6CH42TkwNujooMwuwk06GuAV0hVCOw6yQieejraeCVcVFSsKCcKas6lDoiEOALA1vhXxAPt5f5bew9yekMPwyTyFZteyUgcdDpCn32EvIGpPEtSDgc6DHDibxDgJwrLkKBNOcK5ZJkE4e5jrEa4mppAjbl1Oa8Lz+RB8tGzgIBMWjjMs8oFiduFx5nZAAyZik9zzKLj2pA6bwKRMM0eXlPn5Rc6oQ1V4NmGbi8powPpM4W5BOwKA/tWEN6V3tKIoeN/73gdJknDffffhzDPPBABce+21OOecc3Dttdfi7W9/O44/3rzmUq/XccUVV+DIkSO4++67ceGFF3Lvs1HA+0YTEZaNTBhkUHujRWktiNEgTNEmygL4RaFQrWOhwNZAjTKylUIVWbABIaw6M53n+oTXasKSJOGEoRPwWFv2e3+VzBEOikfJ0RGG8ZAfkWDneldCCjDDAfoThGexELGWCUeCPn6Qw1IBp25pfA9UmDUZHwTavrKCLEMrpekZ2BG0Jmw6SYlapQYTWJH4xddJJqxpGpYLNYyqGrK+1qfIE79zK4iH/JAlMKMGReKhWeLQtlUOCTd+FNyGyMCyUkdSDgP11u+adevcy88LjToo3FRGAzzd33BaUxEOuFd3Bnj2BzD26HYbmzITvueee7B//35ceeWVzQAMAIlEAp/61KegKApuvfXWjq/z7//+73j44YfxiU98ggvAAOD3b5w9Cje+jVr+2agJa6TvU/aVWyf1xKkAnfvbjgGaCfPmFTQIG9HRy4UKchp70QYVp5kwG4TLNbU5hoxS0ivESnIqIv7u+PYka+45dKZwzsWRckJUC0AxhUVyvlKjjnaYtSnRBWnr4CBzW5EkVBxQ7PGQDTpaUA9eJnOE/ZKf1zdYQKFaR0VRESUjGp1Qt1bHGc4QlfJ2InYzAtee1CEwJIkbXtatedb5Bc43WhiEe5wJA72hpOk5PxwLuiowM8PGiTI2sHv3bgDAJZdcwj2m33fvvfd2fJ1/+7d/AwC8/e1vx+zsLH74wx8inU7juOOOw2/+5m8iHo93eIX+gcuEFWKYYNGoAwCUGnshy762EzAYbaikU89DCJIJx9esK1u1U42jzoUTlAAs56vIEeciyQHNCfB9wkDjYg0HfB0HfE8lxaPK7Bp16Ij7wkBbfMm7OFJOiMwhAOAsKyejxnTncWNx3L+vlfnp4qyKUsdKgT23tg/ylG++tAy7ZB03Sck0E+48R3goPATZbMNogOW1zVWYBOG8Q+p2IBJolj8AcZA4Uk0zKc82g40fhVXfaB3JYIIdZ1hz59yr5OaQ5YIwT0e7HYQTBjOFjdq0nIK2J/VLlAVs0iC8b1+D2hHRzUNDQxgdHW0+xwyPPPIIAOCBBx7Axz72MVQqrbN3bGwM3/rWt/DGN77R8O8rlQrzN9msswBiBVwQrpB2CouWlQBQrrIXsiaXUFfrLXps8jSTIMxmwpIkYSwRas0UlUtQiLWgeSZMLloHgh+Ab+oHgHSpcbHSTJhiaugVwvvtGnXoiAeizEKYd9D6YgtrAcuqMAsAjjPIhKkQCAB2DPOUb6G8CuvbvgbidlqUeqiMXl7bZATrPrSPaMyRPlirsNKmNF8vot0ybEpgrCGC1QlKOigzkHVgMSrCco7vN1YVNkkJ+CTX66h+n4xo0IditfU7ZXpg2MG7ZfWHigY2KR2dyTTqHAMD4lpeMplsPscMi4sN2vTqq6/Gn/7pn2J2dhZLS0v4whe+gEwmg8svvxxzc3OGf3/jjTdiYGCg+d/0dOfZoE7BTVDiLCttBOEynzXm22krqpBuxwCfNbYHJ9nPU69GwixRJuyk/xRoXKx016xnJ68YfAUkkwrmFpeMOnRQIVhO5etNriI9g4oErPqsCbMAsWGHqmrcYhQJ+DAaiyJA264cZI0cHb1eQXit1t+Yk9yC07IBP8SBfC61jgVSApkcOLbj62qaxg9v6ERHEw/0rOpOEF4irm9+yABpL9wyGOFGirqBfkxSWq8eYWCTBmG3oK61+PzWb/0WPvOZz2Dbtm0YHR3F1VdfjY997GPIZDK45ZZbDP/+k5/8JDKZTPO/2dlZw+d2C26CEuOiIwECpyYj5EuCOku7EQh1zmrHIL/RaA9Okp/NZAdDgwj6xLXU5UKVM+tworptvhc3xKGx2EYDURxjYEsJAJMJsXORXaMOHQlihpJ3ea4rh/QMFn18/WrcZGO2kwThUq0xyIETZQ2EIUkSYkR1W6g6aVGyYVvZQ7csnY72qUR568AFDOCDBM2EtfwiFoioaWKk8xzhfEVBqcYG7450NLGHdWucYYrU44d8cYBszNxuT9LRD8MO3i3LXYGZGTZlENYzYKNsN5vNGmbJotd529vexj321re+FUCLshYhFAohmUwy//UKtM460m7UER1uGG1YRDovQdPYn54Nwgb9i7ExIMCfnO3BSSKZsJlRx3K+gizNhGtFoO50nCFpU2q7WM0o6SmLwxssZ8JEbZ3XetPb2ERmFovk94/4I8L5yDomkiHEBIMcqBp3Yi3zisnsd1twYltp1ayjXhP3CLtMR8t1MieZOkJZRCdhVjr1PG8OM3JSx9cVuWV1VEeT682tcYYpsukaF2yA3Dbq0NEPww4+E/boaFPotWBR3Xd1dRWpVKpjexIAnHhig4YcJOrP9vtKpR7X8yyio2+0DSwXqtDqREXZnoHGRoCkIDscFAuYxtpUw5SONjXqyFf5mjAAVJzRgpxhR5tYxkicNSQJ5iuvgbYoWRZmkbnMedLv6joERh0T0QnTCT2NQQ68fSWXCa/V+KjiO+9AdRuzGoQzhwCNBI/B7dxG1GkQbjIcpFUvV3d2rXeqCS+ssH3pkgaMmijXdVAqOmGhRS4Zp+MMJceb2iYqeSxROj0+ia2D7HWzrWeZcO8NO/jNp0dHm+KCCy4AANx1113cY/p9+nPM8KY3vQkA8Oyzz3KP6fcde+yxTg/TNRRrRZQUdoFgfKMdBGGQIMzVw0SU9IC45j2aMKajzXyjU4UqchAEQId1YXqx6r3CgHEmPGWQLYotK621KCUIJZiXNKAHBgNNpGeFQbgTqDjrwFIec3QxWquNxQJkklLNftYosq0UGi9QKjqUBCJDrrll6TVhlV4DDssGXE2Y1Czn0y8yt8cgIyDzJSEKqowesyAWShIDkLwso97tOMP8AlLk/BqNb8EFJ7LX9tk7nI6VNAcVXeZczoSrisptuL2acAdcdNFF2LlzJ26//XY8/vjjzftzuRxuuOEG+P1+XHXVVc37U6kU9uzZg1SKbcZ/73vfi1AohH/8x3/E4cOHmdfRXbfe8Y539PSzWMFqhRfBdJMJrxSq0Iiogg6HEJp2COrBAGsob4eOXilUUEIICqHGnQZhbqZweyY8JM6Ep8Li48uWFW56jdVMOEaCcE6SAaVH4qxaGcjPczVhsx5hHXwmXDCcJEPFZvm6/c9DhXOaBkb12oSgHgxJcpGObmyu6JzknMOyAa1ZcpkwGSc44bNG21odYcgci4DBygmUzbYg6BEejU/hTy8+HhefPI7tw1F84pIT8OpjhgxeoDv0eqYwzYKB/rllAZs0CPv9ftx8881QVRVveMMb8IEPfACf+MQncPrpp+OZZ57BddddhxNOaGU+N910E04++WTcdNNNzOvs2LEDf//3f4/FxUWcfvrpeP/734+PfOQj2LVrFx5//HF84AMfwEUXXdTvj8eBZgABSIi3ZxA22pOUuorVooCO5oKwIBMeFIubmEw4QGpHJm0yjYxE4uvCjnuFaSbculgnY5NCYwejVhEqygKs14QTJAAWZAlaKW3pb21jrXa6QIw6zL53HfwghzxXG5tqZsJsEC6o9rNGSkcDBtaVa33PTQxMQ9M019XRNTJT2GnZoBMdPV9izWsmgta0I7QmbIUipTVhAMi6EISpW9ZYZAzjiTBu/sPX4r6/uBAfedPxpuWPbsDVhF2mo2kQDvlloR1pr7ApgzAAXHjhhXjggQdw3nnn4Vvf+hb+6Z/+CSMjI/ja176Ga665xvLrXH311bjjjjtwyimn4Jvf/CZuueUWjIyM4Etf+hK++MUv9vATWAfNhIfgY3WJNow6Vos1aBq4IMzR0aI2JSM62qRFySgTLlaVZhbkVq8wFWa114QlScKJA8dxfzM1uEP4WjQLSYT9lq3y4iQIq5KEInERcw1r9o7UqMMaHc0GoSMZXh2tL/xxqvjWlMaQBRugtpWAgXUlF4S3Il/Lo6ayi69jdfSaMKtCgnBOciZi4luUSCZM+o8nTXQS7VjkLCs7bwIj/gj8dJyhg8EUDAS+0WZlJrdBGRS3hVmi9qRebShE2JRmHTrOOuss/OhHP+r4vOuuuw7XXXed4eNvfetbm2rojYhlYqc3Qkel2egR1qk4jYhSstzM4GOA+CTQbmo/frLwNc3U0YZGHW01GK5X2GEmbOQfrePEyASo1n2LgUqVa0+ymAUDQEIQHHKFBeKS7RIyeiZs3ahDx47RGCSJLVcr5NzSa2Mx0n9alNaGOEStB8KQ34egX0a1bTKVsE0pS4PwNi4LBoChkH36U1W1piNYmTg+5SQJmqpCku3lJqI+YU3Tmgv5Qr3EpDsTsS2WXpeO1uukjAbWbDQhYwWt37HbcYb17ByWKR1tUmZyG70WZhltPPuFTZsJv5zAW1aShcsGHb2yFvw60tGSBFxyA+BbCz5nfwgYEtPRsaAP4YAMyBVIsjW3rHZrRPcyYXNa8ESfgI5OirN7p+1JABAL8OE2X+xRJpw5hDrAZSpWasLhgI9TuLZDllqbj1iYKL4dzhS21KaUIe1JST4IR/wRRAP21biZUg31tY1GQWWDsCJJKDvwxKZ0abWutibyqCrmwX7GSQP2hYKzrLTo4pRk56sh2+UozXTuMOokM+xrEO6xWQelo/tZDwY2eSb8cgEXhGtESGBDmJUqiIOw0C1o1zuAnRcC9QowYGyzJ0kSRuMhHCauOoCJb3ShFeQ4hbRTYRbxj06TkXInaDwdatQj7NSoAwD8sh8RDSi1rVv5bhWqRsgewrLPxy2SVuhooCHOalqOEozGQ/Cv1QJp21VBdjZTOBbyN+lgQBCENY3vER7Yyg8w6VKUBQD5Op9J5wtziNgo7wAG4wxLNUSCPrFRx3Bnow7A/hhDHUk5ALSZdGQFwk47SBVY10AJzr9/J+DNOtymo9nvuZ/KaMDLhDcF+EyY7ARtBOHlZo9kh0xYR3zMNADrGEuEIJP2pEQgYakHl44zdEuYlSsrUNoUzidUythaa13AJ0tRQ0rTaXuSjgS5tPICOtUVZA5x9WC/7Le8SNI2pXa0L0ZUmJV3OFOYa1OidHRptWHY0o7kVt6sxmF7Uvt5VxAE4Vye30h2AqVLgRYLk14WGHWMdjbqKNfqXCuOFToaAJI+WmrqbpzhEpkPPuyPwS/3L3/reSbs0dEeOsHUqAOwGYQt0tE2MRoP8e1JBllw+3EA4MYZutWiBLAijkB2Dv9ncQkXF4r4zXwBnx85x1CA4dSoQ0dcIsMKymlbf28ZmcNYpPXgyLjl6UK0Takd7YtRPEjU0ZLs6HfqOEmJirIgAcktrimj28sgKgIIkxp4TsDmdIJPljiaXQ8UC8vsIBRJ0xwZdQA26Gg/S9NnuxylmSLCslGD+du9At3kVJXWmFI3YNQR0C94dPQmADe8ob1/NRhvjB+0iKYwywodbQOiIGzultU2fcolYZYoI0kXqxiOrWWxmUM4sVrD/1pc29m/2jgj6aYmDABxKQC09Z3mutzkCKFpQOYQ5qP2RVk6zDLhKSYTZp+Xd0hHd6wJUyo6MQn4AlwQHok4Nepgf9eYqqHcNnQg72CmMNA499qV3royfyFzgHneKHyOjDrCAZn77gyPJRAH2v4869COEwCg1pGqFwG0Am8/68GAeEJarqxY7lYwg6bxQ0u8TNgDB86ujzHqsHdBNDNhgTpa6F5kEQ062o5Rh/vCrHDAhwi5MNt7hUW1RiN0UxMGgLiPfX6+y02OEKVVQCk5MurQQduUmNdJGgfhgkM6uqN1Jc2E18wnaIeAc8tKluGIEaOYnEMRk5F/9HyO/TyTPmsLvGiEodW2mSTpQ846MFZporiMJUKnj8XFOopeIREWMVzuUNLpYo1R6wNeTdgDgdCkgLGstJ71AK0eSZoJK5rCWWPawVg8yFtWmmTCqYJJi5JDOhow8Y9W60CWmBYY1Lo1TXM8S1hHnNTCcy4NV2eQaUztokYdVkVZQKP3lNZpdbSrRKljVkmWUS85GGfYaZKSoEcYEJRkXBBmAUCEiPVyDkVMAwauWQukPWgiYI3KddIjrCMZHmRudzVTWGDUMRo33rz2AkG/3Oi+aINbbUo0C5Yke9+1G/CC8AZHrpaDorILFTNL2EZ7EtCi42gQBrqrCzfoaOu+0Qwd7eI4Q6pUbfYK5+YB6oiUFAfhTKmGWp1lBexmwglSl3M6occUeo+wzzkd3RjkIKakJ03oaAAoOMgabdPRawYxbrtl6YhJRMznUMRkJB6a54w6rDFXXCZsY8h8kojWsuiifpoT+Ebb3Pi7gV5NUqJBeCQWQsDX37DoBeENDtqaAZBZwg7paDpBBuguCI8l7NaEzTJhF4OwngnTDMsXMvzuRJaVIzbV0ZyQqZtsxAhrAYsKs+zQ0YAxJT1hkgkDQMFB1tiZjqY9wgaZsONZwmwQjkpknKHDmcJG1pULdXbzNRG3ZtQhoqOtIkmEml2NMxT4Rptd171Crww7+PnZ/c2CAS8Ib3jQxScKGZH22q2NXWlFqbeJR2Ro9Q6uWTYwGudrwnG/eKHUNI3UhElW3sVxcP7RehDmXJi2NrgnAegCOBAJIOS3JwKJk7pcTu1BEM7MQoMzy8p27BztnAmLjDHyTtTRnVqUBHS0oipIk4zSLTo6RsoGWQcjGgGDICww6pgYONbS63WVCRMmJCtJjUEfTpBf4Ixg+i3MAnhxlls1YaPRnf2EF4Q3OLgMQCOBw0Z7UnvgA9xVSMcjGiQfe0L7NLFRfa7CTijiMmGlDCjOghbnH10yyIRNep+peMdujzAAJEJs7S+vukOfMcgcRlaWuT5U20FYkAnHQ34mYMqSjBhR9Rac9AmbtSipdYAOGxjYxgVgoJsgzP62Car6dqiLEFpXFpY4o45Jq0YdXE3YRiZMhFN5WYLqUHBWyB5BiQqzNkQm7M71tJ5zhHV4QXiDo2OPcNx+j3ATVg07LKBU56lJtSae1UuPg1NHA86tK7lMeO29BFaIRui2PQngvZbz3dTljJA5hHmSpUiQbC+Sx43zmbBIIRqTieLbQdZIa8LMFKX8IkA3K8ltnDJagoRB8v1aQa2uci5qA2QwRc5h2UBEl2YERh0To2L/dQqejrZ+Dg4kWMpbkyTH4wyX8rRv23l7WDfolWEHN7zBC8IeKNx0y6K1Tj9oU7/zILxUYlWgmhpEviSmcGmvZk0wYtCtIQ7OMuHu2pMAfohDDho7KcENZA9zgxuGw8MI+OyNYTt2JMYx86LFKOZn7ys4UHzTmjAzRYmKsuQAEBvjroHB0KAjx6ZVkgUDwFCEMhb2RzQCYjp6XmDUMRaf7PhaVUXlWCtbdLQgSGbzc4JndkaKeJ7H5IAjz+5uQa0rcz2ioyf63J4EeEF4w4P3jSY7dTsTlEgGGpTJKLcu6GguCCsJpAriC4WjBONxwEcoX8euWcQ/umRSEzaAG5lwnCjD87IEVF1sU1pruZoj7UlGXthmCAd82DbEsiIiWi5OFN+Fun3q1rRFaa3lqonkFkCWXVNG0zKDLAHDMaIk1pzRnKIgvJB+kbnPqlGHSBhoh44WjjN0YMcJACny3Y8FrM1Cdhv8TOHe0NFeJuyBg6t0NO2R9LNBuJtMOEX8ZVUlwQWz5nGQxXA4FgIILeiWf3TGSB3d40w4TjZHeVmG1kX/M4e1lqvDNAg7NFKgCmmRdV+MMBZ5xb7Yh9LRpVq95e9NSwZG7UmO5wizv+tQNIgBEtDzDpXEHB1drmE+x24qJmVnRh0Bn4ShqHV2Qx9nyByPwyleS6TkMNrHwQ3tEH2/3aJcq2OVlCf6bVkJeEF4w8PUqEMOAKQx3ww0A4372UW1G3X0UpFmwknhjh7g6ejRWBAIkyDskn90ulQDaiWATjGyURO2M0tYR4K0CSmShHKXc10ZrG0q5ggdvcXirFqKS09jg/ebT+HFXXEShAuoA4o9+pbS0QBQqK5tLA0czXrVIzwSDyJO/M1zkrOSATXrKFbrmCeBbyJoLYukoqyxeMj2kHlunGHZgR1ntYiURkSKNkV/biFB1dEutCiJ/LnXg472vKM3OLgRboxl5Zhhm40IdBFKhpJAG6Poak24lkDKKBMu8IshqsRJyKEwi9aE08Uq1PQhfrfZQ8tKAIgLNkeF/CId2ugca/T6EZcy4StetQ2qquHx2TQuOXUCp08Pcs+JEeP+5kxhv/WWFUpHAw2F9EAkYGhZ6Z5bFjnvYiEkCGNRkGXUa2X4AvYWY5Fv+XwlzaQ5Ew6NOsYcUKRJOciOM3QyQETUnpRwtsnrFr0w66CirGjQZ9mf2014QXiDw5SOtm3UQei48AAThLuqCQsy4SWjTJgLwiGg4BYdzdaEVQ0oLc+wwxLDA0BIrNxWVY3brDiqCQvMLXKlJbjWYblG3dJMeKtDS0FZlvDOs7bjnWdtN3wO3Vg0ZgpnbJ2HsaAgCOsLqpFlpVuzhMn5OBIPcowFAOTz8xgYOtbWa4tmCs/Xi0wQnnRs1OGAifGFgDaXNkfjDPOLWCLn15jFz+A2emHWIVJG22Uc3IBHR29g1NU6b1LQTkfbtaykwY8oQ93MhFUlYZmOHhHS0Q4zYcFiWEm9RJ40bfj36VINitqdZSUABH1BBAmzmS+mxE92gswhVAEsuSDMsoooqdsXJMl22cAnS4gFyZjHii6e669l5Wg8hISAOcgX7CuJQ34f8TfWsOjQqGMpR3uE7Z9/3DjDmoMNtigTNrGi7SV6Ydax3nOEdXhBeAMjXUlDA7uSM77RNtqTAH4RGosNMre7qQlTYZamJJDKVYWTmUS1ORBzC6eZcCzog19md7O1Faq6tU5FN4/PAeLk8sqVnRkmCJE9jHk/n1Vu6WGmQq04m3S0TfDWlWu15TwRD+kTlEg9cyTsrE+VCrNGYkFEIyOQyTmaLzgTMbVTpkPIdmHU4dyysnkshInJ1hx4l28QtyyAz4TLNZWbfmQXc5xlpReEPRDQDAAABhnfaOtBWNM0bhGajJNeVie7ZQC1eo3L2DUliVKt3hLdtIFfDEOuCbMkSeIU0hptfbHRnjQYDTg2dE9IJOMrO5vQI0RmFocJVZgIJJAQ9Vy7BEqxF2TJEWMhbFPKHQHIhtNQmOVQHU1blIbjQUiyjDh522zBmYCunYWZ8M3xRh0jDo06bPQI60iSTa2TcYa13BGsbgDfaICvCQPd9wpvBLcswAvCGxp08RmADOZUtBGEi9U6yjV257h1YIi5XVJKqNXtn9g0CwYadDQATpylqhpnRDASDzbqtO3oop2HUtKywArRCJwoy0E9WEec9ITmu2AaOGQO8z3CPZ7zSicpOc2E+UlKNb4eHIgB4UEUa0VuxKZbvtEjscZvmwDLnORLDpTEYM+7oSBLrUuahrGEtd9nMUeDg/1zcICOM3RgQrJMZiED65cJU3U00L04i68J9394A+AF4Q0NLgMgtUo7NWHOshLA9kH+gspU7Qe/xRJL32mqv2mJSYNaulQD/RgjLvYJA7w4K1QgQbjHlpU64sTm0SnTwKFWAoopThnttD3JKrhMWJIdbZZ4/+i6oEd4GyBJWBVManJKR68YeIInSDuP85nCrSAcC7DXhFWjjrqqcRm7IzqabFScmJCkiMGHH7Iju1A3EA74EPK7O1OYn6C0STPhUsn5IPhf//rX3b79UQ3espJcSHYsK0kWEPLLmCA1YcCZQjpV5OvBWMsuaFCjoiwAGHZRmAXQXmEN0dI8+wSTTJgqup2IsnQkyISegluOWdnGpoIqo/ufCTujo6lCOl9WDB3NqG90UA4KZxt3QqnKl0ZG1jZYlLHIOWnnAVu3DAbY456waNSxXKigTnapjoRZRECVhWrbNpWKLUcDsXVRD+tIuOgfraqagHHYpEH4zDPPxGOPPWb77z7zmc/gnHPO6fbtj2rQBYi3rHQ+vGEkFkTIH0LYR8YZOlBIiywrddBMmO7yk2E/gn7Z1Uy4vVd4AAUEVLJR7LFlpQ5q85hzYPMoxFqNm2bCTtuTrIKbkezQBYzPhAV0tMkcYSeBgFLRQEtwl5BZ5iTnsEuAKYP42deYtGzUwR6nLLU2C3aQJK1XWVlqMCg2sERYsdHgoO3jcBPUP7ob68qVYhW1Orsp2bSZ8N69e3HOOefgM5/5jFAJSzE7O4s3vvGNuOaaa1CruWPCfbSCUnG8ZaV1OnqF1sPWLuwkWRycKKRF7UnNx0jQpfXgZpBzSZgFsP7RWyRa35MAE8MBuknoJhPm1MQObB6FaPYI9689CQBifjYDrUsSKg6yRr4mrIjpaPSuPSnok5vHkSAb0XzV2Uzh9kxY8bNqZKtGHXQTOBIPwSfb33QkyKCInCzbG2eoqlhWWOZmverBOtycpESpaFnqTv/RDboOwslkErVaDddccw0uvPBCzM7OGj7361//Onbt2oX7778fmqbhggsu6Pbtj2rwbllEkh+1XhujwUXPApJ0lJsDOlpk1NF8jNLRZDMwHFsLmJwwK+t46lC7OnqKBuH4BOA3bjmiQjIns4SbbxUgXssOJ/RwyByCAnATlHrZngQAsSBPA+cdtF0JW5S4HmGXg7DgvNMz6gTZXOQUB+08YDPhfID9rSctbpAoReqEigaAJDkXNElC3s44w9IqlkjwH+txuaMT3DTsoMrosUQIfoddEN2i63d98skncf7550PTNNx///3YtWsXvvGNbzDPyWQyeNe73oU/+IM/QCaTQSAQwGc+8xncfffd3b79UQ1Tt6zIMGBjZB1PR68pQ0lLizt0dCsId6Kjmz24lI5Wa4DDzLE9CHOZsEk9GHC3JhwnG4uc5hLzkz2EJZ8PCqFle50Ji1zACg7OF75FyZiO5koyLk1Qau/9poxFzkE7D9BuKKEh42M3zFaNOvgeYYdBODzE3ZfN2TAhyc9jibOsNL92eg03DTs2whxhHV0H4e3bt+NnP/sZbrzxRgQCAWQyGbznPe/Be97zHmSzWezevRu7du3Ct771LWiahlNOOQUPPfQQ/uIv/mJdi/ybAeaWlTaNOgriDI+jox0sqqIJSs3H8ubCrGa9i2bCgCuuWXwQNq6b1gXtU93UhBNkIcxrfM+0I2QOc/XgsC/sOEBZRdAXRID2PlfsMyeUjlZKOYDS2gaZsGNltMgqVT8eshHN1cVOb52gn3eDyGKRKHknrBp1cJaVzoJDLBCDj/Y/F22MM8wvYJkGYYHFZz9BM+FcFy1KG8UtC3CpRUmSJPz3//7f8Ytf/AInnXQSNE3DN77xDRx//PG4+OKLMTs7C03T8JGPfASPPPIIzjjjDDfe9qgH36Lk3LKSLkI6DUyDsDt0dFtNmCwqXJCLGWTCgCv+0Vsk0sNsYlm5WqxyytTuMmE2YOQlDVBVg2fbQOYQjhAqejI22ZdNbdzHfh+Fmv36Kc2EI2VBcHB7eINoctcaEqTtJu+QsdCD8IRvDmVi1DE5atWog9DRDntXJUni+p9tmZCIfKPXyahDBz9T2MVMeJ1EWYDLfcK6Uvryyy+HpmlIpVJQVRXJZBJ33nknvvCFLyAcXr8Pu5lQqVeQJwtcN5kwT8e5Q0crqsItlFQd3S7Y4y0r1xYZfxDwk3PDoTirPROekkjN0oZlpSS11awdgBuTJ8tAF0MyADTq5FneqKPXymgdMaL4zjuon9IWpXiFtJBFhoFg431cmyVsRkcTY4ucQ8ZCV+UPBdnaa8Ooo3/DG3QkCWuRtWFCouXmN4xlpQ5OHd1FJjxPaP9Nnwm345ZbbsGdd94JSZKai28ul8O3vvUtFAou9Um+DLAqsDgccWhZCYgnyAC8MMuuOnq5tMz5W7fXhMs1lenPpP3KTJBzyTWrvU94K5cJWzfqGIoGHVtWAuDH5EnO+moZlNNANe/aCEO7oEG4oJRtC+hoJjxQJZlwW8nArUw4ZUZHk+CSgzO2Qs/U4gH281g16gD4mvCYQzoaAJISu4HM2jAhyWQPcZqDsXUa3qCD6xPuJhPOsO1am7omrGNxcRGXXXYZPvrRj6JcLiMajeKGG27Azp07oWkabr31Vpx55pn41a9+5dZbHtWgi48PQIKho61fECKryNGYuEXJLh1N68E+yQ+tzi7U7cHNLCNxq1dYF2bJUDEBsvDYmSPcZctCnAxAr8gyanbaREQwGGHYa7csHTHaKwzVtoAuEWIX02GFDm5obJRUTeU2o66NMWyno0mXQU6WHCnzdQYmGGB/4wnZ2nmkaRq3EXRKRwNAknoA2LielvKHufuc1uPdgqvCrA3ilgW4FIS///3v47TTTsOdd94JTdNw1lln4fHHH8c111yDJ554An/4h38ITdPwwgsv4LzzzsP1118P1Y3a2FEMGoSHNIn9sWxkwtkyP56vaVTQJR3NuepERhANsousHtxqdRUZsntlhE8uuWYlwgFIEjCGNAISoRZNasKcUUfCORUNAHHBzOJc3oY4RoQ1FfF6ZcJxsmnL6zOFbSAWYjcQE5pYwZ6tZFEn1LBbfcLtm79EjO2prUkSKg42S1F9gpef/T6sGnVkSjVUSRtiV3R0F+MMl4rsxmhQDiNgoxujF+BblJzR0aVqnaOyNzUd/eEPfxiXX345lpaWIMsy/vqv/xoPPvggjjvuOABALBbDrbfeim9/+9sYHh6Goij427/9W5x33nk4cOBA1x/gaAWvjCablph1YRadIwwYC7O6DcJjkTFOUaz33q4KjqM9I3ErE/bJEpLhAK+M9gWBqHFdizPq6DYTDvItPXmyuNlG9hA0rGMmTOqnTiYpUTqa6+U2mJ4EOAvCoglieoseAMQFqt9c3v5MYUmSMBAJoEaNOsLWaqm0Hgx0JwxMkvMva6N+v0wYiFGLG4lewi2zDirKAjZ5JvzFL34Rmqbh2GOPxe7du/G3f/u38JGCPgD8l//yX/DUU0/h4osvhqZpeOihh3DmmWd2+/ZHLTijjhoJYF1YVsZDfoQDjd+o2yBMfaNHo6PcwqH33tIgJ0lk2IKbrllRQRBObgVk41OeN+roLgiHfWH4CauZczihp4nMISzLMjcmr9dGHTrihDlxMkmJ0tH879TIhOkc4UQggaDPPjuRqyicRSGTCQtYBKeMRTISQNHPnucTFlkKWg8eigYQ8vNrqeVjode2jbLBUo39Tcd63P5mBQNEmFWs1lGjyYkFUCo6HvIjTtrm+glX6Oj3vOc9eOKJJ3DuueeaPm9qagp33XUXPv/5zyMUCiGfd2YP93IAnwkT6sVGTdhIlAXwdHS+moeqWT+x6QSl8cg45zKlBzfOtSgaZC35RK5ZDjEYCQgyrP4ZdQCNzChOLjGnY/KaEIww9Ev+vrWPuDFJKRyQ2353zbCXu1fKaIDNhIPBKEKkBpwrOGMskmE/Vv3s9TOZPNbS31IXJ6c9wq1jYfvUs5pFx7ZaGUukTWvUBvPWK4hnCtunpOn3vJ5ZMOBCEL799tvxr//6r0gkrA8T/9jHPoZf/epXeOUrX9nt2x+1oFkA5xtta4ISP7xBxwAZ/q1BsyXOEmXCNIPU/aNNRVmAy0McgraU0YC7wxt0xDlzi3R3L5g9zPUIT8Qm4JOdZ0x2QCcYNehoe0FYkiTEgo3jHUQeEYkEB9d9o9nfNRb0IRJkv68EYSzyghnZVjAVKmGJM+o43tLfcu1JXc63TZJNi+VxhoVF3qijTy1wZqA1YQDIOaCkN5JbFuBCEH7nO9/p6O9OO+00PPzww92+/VELqgpl2pMCMUDg42sEQ5cq8JQVYE8hLaoJc3R0MxMWW2c24XombL1HGODV0aNdZsIAkCCtKfmKc4odAJCZ5TLhflHRgCgI26ejgVa7iXjARoO+da09yag3vQ2Uscg58MQGgEn/YYFRx6mW/pYadXTLxCQJO5KDZk31nV/kLCvH1tmyEmiMXw2SlkEn4ixKR6+nKAvoQZ+wHQSD3alPj2Zw6uj2TNgGFQ0ILPvaMuGIPwIfbeq3URe2JMxaC250MzDcw0y4URO2ngmLLCvdmKoSJ+0pTif0AADUOpCd45XRPfaMbodbM4X1GhwXhBOTTU90Thfh4vAGiqTEfqc5QZ++FcRltrWnO6OOLulo0ThDK+efyKhjnXuEgQaDwht22M+EeTp6faYn6VjXIOzBGKaWlbaNOoxpYEmSHIuzVE3lDPZFdHQrCBtYVurghFlpS8chgt2a8HKhAtLF1XWLEgDEiQtYrtaFYU1+EVBrOBJYv0yYmyksOcuEdYU09xsl3Tfq4M47wWSsOJkp7JSx8IF1yxpUJcutPUsuDW/QkUywm7OcLEMrWthc5BeQ8m8stywdbhh2HHV0tAf3oWlah+EN9kQSlGalNLDTcYYr5RWuj3M8Mi6ko4VtIjTTdJGOHg5pGJPI35sE4VSOXahlSUCXO0DcBZvHJtbG/dGacL/akwBRJmxfmAW0xhmaTbmiuoiRiEvDGwS/a4J4Ymcd2ovWVdJfW7e+kXPLN1pHkvQ/1yUJhULn1qtS9kjjd23DevtG63DDsGMjDW8AvCC8IVFUiqiQSS5sELa3K+VqsSQTSJC5t1addahblizJGA4PczRuRVGRrygdj8NNOnqCqzXCtCZMldHDsaCjYeoUVE2cdzgmDwCQaczqpjXhfhl1AAJ1tEM6Wp+kZMZWuFcTNu4O0BH3RZjbecUZY1HU2EwzqkYMnsnDdTqa9HQDQNbCTOFUjp8Jv1Ey4W4NO+qqxn3Pm14d7cF90FoYQIRZNico8ZZ95pmwVTqaTk8aDg/DJ/uENG4qXxXMNO5ER2cd2QcCwHidPbYcovzrtx9fD5TRABCnLEPdYpuICJnDyMoSl6VsjfVPuUqDcEmWoTjIhA1rwu10tFs1YQvCrCTJ8HO1EvccK8io7LXjU6x1jeQrCopVwip1SUfHAjHIdJxhoXP/c6rADtSISD6OAVkvdGvYsZyvcO6BHh3tgQOl4cKahEh7MLJRE1bqKtKkbkIzAaf+0TQT1imraNDfbEHRsZSrmKq0AfCZsFYHas7o22EShOc0cyrT7R5hHYkgS7E7HZMHAMgc4rJgCRImCe3YS0QDUe6+ooP6qTEd3QjC1XoVOWKz6NS72GiWdjtordspY7EC9u9qVcGcbAEWBS5O3dLRsiTz4wyLnVuvlqjOIxDfMLPfOWGWzZowrQf7ZEm4KesnvCC8AcGZ1msaeynZCMKrxRqXTHJ0tEP/aN43ukVZ0faeQ6tFZpoSIMqEBQuWQ9esZJXdzR9SR0zddWgm7IYyGgDiEdYwIe9wQg8AIHuIU0aPRcb66ulLM2EAKDgIwvGw32DAhrhHGHAvExapo+lmKas6YCw0DUtgg0KuMsqM8jQCpUjjIT+iwe5dnKjq28o4w6Uq+3uOBge7Pg63QDNhu2YdtD1pPBFypezUDbwgvAHBtScp1C3Ljm8070c7HDXPhK3WhBeJD/J4tHVclM59foHPrjtmwoBjcVa0xNJuc9oINzyiHb3oEQaABBET5aE1Wo2cIMMbdfSzHgyIM+G8AxFTIuTHKDL8gI2kOAj7JB9XNrGCuqphpdhZmBUPDTK381aNLdqglVaxQPpYV6uTHM0sgttGHTqSMqVvO6ijNQ3LpB6+EdqTdHA1YZt09EZzywK8ILwhwQlSFHKideEbPRQNwE8WCqc1YUpHt2fCNJPcM8cu1AGfxCkd4fM3jEja4VCcFSqwApTD2gjSReMLltLRIsrSCeJE0JKXJeeCswyfCfdTGQ00KM4YGZFXcNB2FQ/7eUczOdA8t7mNaHgIsmR/uUoXqxwTJPptk2Sz5GSmcHZ5H2fUsVLbarr500Hp6G7rwTq4cYadru3SKpbI1zzW53PMDJw62qYwa6O1JwFeEN6QMG1PAuxZVgpUvxSUjrZaExYZdeig4qzn59nXHI4FxXUml8YZyjnWNKGRCRtTjLRFya2acJz8VjmHLT1QKkBhcV2V0TpitO2qXrQtoIuF/IIe4S3NARuu9QgLJncNCa6BOJkpnJfsCwLnU88xtyVNQ7U2bC0Iu6yM1sGNM+x0bQvcskaT6++WpYPrE7aZCc9n2O95vduTAC8Ib0jwvtFtu3LZDwhaD4zA9UiKlKEOzTpEvtHNf5P3oTtQwx5cSjk6MezQtObcXR1HtFGbmbBLQZhQeSVZhmLFMIHCoEd46zp4+sZpr7Bk0YmpDQlREG6b9eyWMppuQgejAQR8/LJHf6e8JEFV+FKOGRbS+5nbA3UJgN+SeKhnmTCp4XccZ5hf4H2j+yj864RuhVkeHe3BEmgWMML0CI+ZjuOjsOIW5CQIa5pmmgl3yiRFvZoAeHGWE+q2nOGCwhEMGwbhWl3FarFHmXCQb1EpOJkpnGkEYS4T7qNlpY4YURIXJWczhbdQb++B3rtlcWLANVBjC02SULDQztOO+Ry78Usojd/KUSbsVk2YDGjJdlJ9i3yjN1JNmMuEPTraQw/AW1Z2Y9Rh3iMMiINwJ0VnppJBTWUXFzNhFoXRYugKHU2yYFWTsKANc61aOlYKorqhWy1KfBDOFZYEz+yAzCGUJAkrZIHsp2Wljhg5X5zMFI4F/Zy3t9bWI8yxQS5NUDJqR4mLZgpbMLZox3yRDdohpbHArysdTccZdlB9K7kjWCFMwUYx6gB4YVa+okCxMVN4o7llAV4Q3pDgWpTaTzLblpUdXKrAB2FFVVBSzM0KaBYMsH2cHYOw0eNuuGZl2XpwCgOoIoBMUbwA0RGGPlnCUNQdYVbUH+UMExyNycsewpxgwPt6ZMI0u3cyzjAR5unoapsAiGODHFpW8pO7xL9rLDoCqcuZwgsV9rr11Rrf07oKs8jmJauZK7VXsjPQiFZjQwVhwUzhfMVaNlyoKMiR53p0tAcOqqZyQZidoNStW5YgCAtaPzpR0jQID4WGmH7VTouIMR3tRibM2u4d0RoLkVEm3CvLSmBtdi4xTMg7GZMnUEYPhgaFLUO9htg/2iYdHeLp6GKkRQn3SphldN7Jsg9xslnKFe0xFguk3qrUBgF0pkzLtTr3HNfoaEIlZyUVUI0zx1Se9Zb2QXL83fcCtCYMWFdIUyoa8OhoDwJkK1luKAKbCdvblVoRZokMGDoppLn2pCh7XJ0y4VHLwiwHSuIMmwkf0RrHZlQT7pVRh44EMUzIOxGbZQ6v6wjDdnCTlJzQ0b46xqU0c18+1Bq9515NuHM5Rgd1l8pbMLZoQtOwQNzQyrXGeddJPESZGAAYc4uO5sYZmv9WKbLxGPFFHLWG9QqRgA9+skG2qpCmRh3JsB+RIM8u9Rsb59v1AMDAKaiLCUpWhCk+2ccF4o6ZcNFYlAUAkaCPs65sh6hVCoA7wixSE9YtK40yYUrZu2XUoSNODBNyTsbkZXg6ej3qwYAgE5bs09HB4jx3XybQCBiapvXMN9qs/zsO9vvN2WAstFIa8z42OGSUxiapEx1NpyeF/DLfQ+8QSXKOZGUZWslYnb9EywBBniVbTzRmCjtrU6JBeCNQ0YAXhDccqCAloQHMsmGjR7hcq3M1EKNarF3XLDNldPM+k2BmWR3thI7O0ky4EYSt1oTdMurQEZfZ78GJwxSyfCa8XkGYn6TkoPeZ/EZ5LYyM1qDWC7UCqkRA5B4dbZIJ082Sjc9kZNQBWAjCdI5wMuSaV3OSbNrrkoRint8A6UgRv+4xh37dvUTCoWEHpaM3gigL8ILwhgNv1EHqN3HrQZhS0YBxgOEMO2rmgYLLhAVtDGaUtOFjbgizuJrwWhA2zIR7M7xBR9zPXux5uw5T5QxQyfKZ8Do5GdFMuODEBSzDm6nkKg3Gx03faH6WtvEGKyGzj+Ut9ssDwPzyHua2pGmo1BrnXSc6ulfKaABICvzYs6Tu24RSxZJGWvUInb0R4HSSEu0RnvIyYQ8iuGlZSYOwT5aE6kJAYF3ZYVE1s6xs3mcShHsmzFLrQJZdZI50oKNpJux2TThOXItynQwTKDK6Ucf6u2UB7giz6EZpThtGYY21oddAxB9xJECrKHXO4N/wvAOQIBaPuZp1A5KF9AvMbd2oA7BPR0+4JMoCGqwFNf8yHGdYWEKKtMCNrIMZTCc4Nezg6GgvE/YggqkyGrBVExZZVsoGql+7hh3d0NGRgM94Qky3wqz8IkD6l9szYVXl+597nQknuh2Tlz2MGoBF2iO8TpkwR0dL9oVZopKB3mqyXHKnR1jEBJkJs7jNko0xmvNZsVEH4ICOdjETFo8zNFB95+e5IDyWnBY/dx3h1LCDZsITXibsQYTOvtHW1dFW3YIAezOFNU3rio42FGUBYmGWSUsFB7K4VzUfUmi8pqaJR5/1yrJSB+2rzdsdk5eZxbzfx/VvbhhhloM+YZGCvRmEiS7C8RzhPM8EDUTETBDAb5ZydfNe+XbME6FZWGkt8J3o0gXKxLi8CbQ8zjC/yAfhqD0haD/ABWGrmfAGdMsCvCC84WBaE44MATZmx/LDzE1EKTZmCudreZRJNifKhOkQh9ZxmAVhqsbU7PkSE5pzXhuG1naap8kQh6qicq1LrteEiXVgXrU5Ji9zmLOrjPqj3MapXxC1KGldCrPmMNzcIB3Os485NYugoiwzJgjgr4F83bp39EIlzdyWa63vqFxTUVGMTTJ6ZdShgwrOsuRYdWi5ec6y0qlJSi/B0dEWasJKXeXKTp4wywU8/PDDuPTSSzE0NIRYLIazzjoLt99+u+PXq9VqOOOMMyBJEk466SQXj9Q6OCpOdbE9yST42VFHi9yyRJmwUW3VTKEqnClsh+qkgh+JXcBpwBXNW3Y7E06EWDo1D5vzhEUjDONbXFPQ2gXNhOuShLJtYRYvntNrwi9mXmQeO3bgWNvHCFgzqmlHgswUzmnWMiwAWCAzeOs11i7SjJKmwWHc5eDAjTM0aJHLZQ+jSjYpG8k3WgfNhEXsFkUqXwWtRHktSl1i9+7dOO+883D//ffjiiuuwIc//GGkUim8+93vxqc//WlHr3nDDTfghRde6PzEHoIf3tBu1GHvghBlAkawM1OYTk9KBBMI+fjAZdRva7oYhnivZVuiH5JhLcvsd0bFWXSEoV+WMGhCWTpBLMIuyDlJA+o2pr9kD2+YHmGAD8IAUKjYaLuq5Dn6eq6tJnwwe5B57NjksXYPEYCoR9h8cxUnPsu5DhaP7eCMOhR282dEmdbqKnedup0JJ/3s75UxEJylsjPcfRvJslIH1ydsgY6mVHTAJ2HYJWvabrEpg7CiKHjf+94HSZJw33334ctf/jI+97nP4YknnsCpp56Ka6+9Fvv27bP1mo899hhuvPFG3HjjjT06amswrQnbaE8C+EzALTraiigLMM6Eh83oaNkH0KEHdqhOkmGlg2yLRZr0CnMtLHFzytIJEnRMnl01cWZ2w7hlAWKHtYKd3meyUQIamXCurKCm1jCbZX/DHQM7bB8jAKQKvDDRDAlCveZgTYuglTJYIEYdZY3dJGUMelnp+Qf0IAiT8oHROMMlMoAiIQWEm+v1BtcnbCETpsro8UTY9evcKTZlEL7nnnuwf/9+XHnllTjzzDOb9ycSCXzqU5+Coii49dZbLb9etVrFVVddhde97nX4yEc+0otDtoSaWuOC37CLmbAdYZZpELYgygKMg76hZaWOblyzCB3dboUI8LQgb9Th/qLDzaqVZcCqa5aqAtkjXE14PTPhoC+IALXirBcb7WFWQBzNVrQ4ygihUFFwKHcIisYuqk6DsJ1yDAAkiPVqXpLAjdcSILu8FyVi1FHzscdslK1RZbTfxeEhOrhr20CdnyKlsDHBZmsjwIkwayPOEdbhjjdan7F7924AwCWXXMI9pt937733Wn696667Dvv27cMTTzyxbnU2AEgLPIWH3LSsNAkwdtTRVjPhSNCHeMjPTTnptBginATa466trJFd4EsRNljRmjBVRrstygKAOFncC5IEtbRqbQdcTAH1Kg5vEKMOHfFAFKttG7WGf3QOiAx2/mMDW9F8RcHBzEHmseHwMAZCvOGEFdAWpU4brAQxpqjIEqrlNIKknEAxv/wcc1vSNESDUwBa6mqjmjA16hhLhFzP0PhxhgamNdUMExHGQuafe73gxLZyboP2CAObNBPWqebjjz+ee2xoaAijo6OW6eiHH34Yn/3sZ3H99dfjhBNOsHUclUoF2WyW+a8bUCpa0oDB9vYcG+1JmqYJqVYj0CBcUkrcvGAdVoMwIFZCmwqzAIFrlsWsUakAZPxcjRhacEG4D5kwpfobA+MtTujJzEIFML9BjDp0xEiWZGumsIGtaL6i4MUsEWU5rAcD9tyyACAucIfKGblLtWFhdT/7PpAxGIkw9xkH4d4qowEgSWl2TUDfahqWCE09sgFFWQCvjs5XFGH/fzu4HmEvCHeHTKaxKA8MiHfIyWSy+RwzVCoVXHXVVTjzzDPxZ3/2Z7aP48Ybb8TAwEDzv+np7hrbaX/kkKaxlvI2xhgWq3VUFLamZUpHi8YZGiyqVtyydIgyy06LoWPXLEGtUUtsY27TxbDXRh0A39IDAAWrY/Iyh7Hk80EhDM3WdXYy6mqmMNcj3AgSubLCKaOdUtGapuGlZTaodFp4E4KNTc7EZ1nHfI7N7CfkkGXxEKWj3Zqe1I4k2SRnofGlg0oWKTL4emydN3pGoHS0poHzyKegNeGNYlkJbNIg7BY+9alPYd++ffjKV74CH+mPs4JPfvKTyGQyzf9mZ2c7/5EJ4oE43jj9Ruwa24Vt8W3YWiMnlg06mlLRQAfzeiqGgjElbbUmDIgzy450tFPXLLK4I5hAJElbRdjvpR+ZcMzPq4lzVsfkCaYnBeXgus94jdFeYcmG2CwrpqMLAjraaRBeyle4Ddcrxs1rnKFgDEFSA84TZkWEhQIbqCcDSS5bs0pHuzVHuB1JsnnP+gQDN0RGHYntrh+LG6AbHKBzXXijumUBm7QmrGfARtluNps1zJJ1PPbYY/iHf/gHfOpTn8Jpp53m6DhCoRBCIfcuml1ju/CPb/rHxo1yFvgMyaxt0NFUGRryy6ajBUO+EEK+ECptBgVG4ix7dDT//XRSqToWZpFaIwa2YYCIXCgd3Y9M2Cf7ENMkFNpMfPNkVJ8hBNOTpuJT6z7jVegf7fB30jPhUk3BgcwB5jGnQfiFRbYNJxyQsXUwYvDsFuIasNJGOmQJ6yPCfIW1mp0ID6PqZwOFURBe6gMdPUD0A1lZhlZcgRRt28jlF3ijjsTGzIRjQR9kCUzfr1ldWNO0DeuWBWzSTFivBYvqvqurq0ilUsJ6cTuefPJJ1Ot1XHfddZAkifkPAJ5//nlIkoTBwUHXj98SRDVDG3S0qEeyk+jMikK6WCuiQKYAmWXCNKglwn6E/B1YB8d0NA3CW7meX9on3OsxhjpiRE2cIwu3ITZYe5IO4SQlK7+TpgknKAGA5Ctw55zTmvB+EoSPG4tbEjwlyZJoZbNEjTomY1s4e0yrmXAvapVJ0lWhSBJKdIhDbh4pH/vZzTbX6wnRTGEzw45cRUGxytLvGykIb8pM+IILLsCNN96Iu+66C+985zuZx+66667mc8xwwgkn4I//+I+Fj91yyy0YGBjAFVdcgWjU/vQWV0CDcCAKBHla0wicW5CF4JIMJpksV0RH03owYC8T7lgPBpyPMxRkwoNREoTbMuGKUud6DHuRiQAN68DFNqFb3urGInMYRzaQUYcO2iuctzpTuLQKKKwns54Jy0H23ArIAcefdR8Jwp2oaB1xyQ+g9Tvlyp03SwuoAW3qjYmBYwDFmoKX0qQ9EWYJ1OXZ/BzaV7ZK9giylI7eoEEYaNSF269lMzp6IcO3ZPWC9neKTRmEL7roIuzcuRO33347PvrRj+KMM84AAORyOdxwww3w+/246qqrms9PpVJIpVIYHR3F6GiD0n3961+P17/+9cLXv+WWWzA5OYmbb7651x/FGHlSi+qhW5YOzrBDEPwoFR31R03HzL3mWLYm+6pjLLQ9OM2EaU04uQ2DEfZzZ0pVaJoGSZKQEtTNe1ETBoC4HATUllDo/2/vzOOjqO///5o9k80eOTbkgBBAQpGIgggocsoRReuBgEBsRcWDWr9abe1PBROEqrX9amupX1tR9FuKSr+CtVQQC4SrqFQERQ4DJsgZEkiyu7k3O78/lll2PjO7O7vZY5a8n49HHpDZ2dnP7k7mPe/r9XZ1KL+xOJmmPk9YfpKSAiPMiKl4eA418J4TGqP4nC+0FkKniewSxYaj+2crM8IWjR7wU79yhXhPfEsjahgPOyejP1qcrCcs9dQ6PbzkHIzmBCUBOXGVRlcNcv1+l1PLUqNutEA4gh1sKDrDpEeKPvwaoFiRlOFonU6HZcuWwePxYMyYMbj//vvx85//HFdccQW++eYblJeXi9qNli5diksvvRRLly5N4KrDhPWEwzXCkglKoY2LEulKST44RBvDgBwLFt40CL0zTRg7IBs/n/KDkOtASrr4d8WFWaE94Y5O3heaqmNCgXpt8Ck7XcGsE+cjnUxIXxZ3O+CqUZVQh4D8JCUFNxbMjVIt0uE+7wtoDOJzqyvtSRIjrNQT1rAzhYMrgTnOVUqEOnLtgyTnkZyndq6pHZ1Ma00sPDStRgsLz4wzZP6O65hWLAM0CRsQooRwBDvYymg1tScBSeoJA8CECROwfft2lJWVYdWqVWhvb0dxcTEWL16M0tLSRC+v67BGOIx8MCA3QUlZONofWSPMVkYrCFndO7ov7h0dRoFNpOFotkXJ1hM2k9SoNrR0IM2okxRlKcmbR4qFmVXrYkKysjhPgQcv1Y1OsFAHIG27alZamMV8R2f8tL1ZIxxpUVZjS4ck11qUo8wIW3Wp8J+vEepmSU6oo4etECcdYuMtlxNme4Q5TmG6JgKsnA5O/zA7k+uuaxFHIbJ1poQKF4UinElKalbLApLYCAPAiBEjsG7dupD7lZeXo7y8XPFxeQVSdTEn2p6wAiPMhqPlcsLhVEZHTCTh6NZGqRGw9YLFqINWw4k8jobmdvRMT41Le5KAmcnnu5TMqm08jgaNRuJpqcETNrE3FUr7hJloxVmtnxE2RscIs16wTsOhMEtZPYVZbwL8TgtXAJ1lgZpzUqEOvVYv8YRdbW64Oz3Q+RU/sTcKWWlG0ePRxKox4IRfTQI7zrC2rQHwu0RkqdgLBuQ8YeXhaDUVZQFJGo7uFnQxJ8x6eZlKwtEKPGF2gpLdpLxtSjGsJ9zuDK1LzOaDAcDa01tJyeSPGs8XdMSjPUnAohe/J1enNB8twSEtytJyWvRQwaB1yUxhpX3CjBFu0J1/L5wbnF5cBBWtyujCLBP0Co2bpC7CHXym8GmnOMedw3nPIdZIANIK3lpGqCNWRYFA6HGGdUzYPTtFvflgIDzpSrWHo8kIq5UuhqNZ3Vyl1dH+KCnMiosnDHh1iYPB5oPTegA670Utne0VPh8ajFd7EgCkMRWqLjnpQJbGY5J8cA9Tj4iLlaJJxH3CTDjaafSe1xr9WXCcWOEt0jnCh2vFRrioh8x4zACYmb8BFx/8ZqmGmTyUo/e+llxtARuSlkhWxrBi18oUTzr8xxl2ulHnYf4W0nKhZsLKCas8HE1GWK1IwtHKPU6Ph5eK1yvwhJWMMwxHsjJiWLEOIHSoU6ZH2PffAD2bbGVqLD1hM1NspmhWbeMJnFBhjzAgUx2tOBwtNsJNKd73w4ais1OzZVXclFBZI75hU1qUBQBWY7rod2cA/XQBVqgj93xFcYpeAwPjfUuNcBw9YT3r4fulQ5pqJUIddktiZVFDweaEg/UJn24Uf85khAlluFgjrNwTdrR2wM1UXSryhBVUR59pFofJYxIaNZgBVhEqlJclUxktEKhXOJ45YXZWrYsD0CE/Us5H43FVVkYDUiPcotHAHSoc7ekEnCfFzzN5PS5JZXSEXjAg9YTDMcJm9nsKMVOYFerIOX+TJCcowYZMWd3oWLQnCUj+tv3HGcqoZWVb1SlZKSDxhAOEozs6PZIiVcoJE6Fxt0l7LsPICcv1vyrpEw6VE27rbJNsi0k4muMAI+MFhbrAy/QIC0hVs7yfTzxzwuw4Q0XhW5mcsFqMMBuOBoCmIOMvAQCuGsAj9ljc5yu9JZXR1siKslraO3G8Xlz0Fo4RZm+WHFyI6TxMuDrXz3iF0o+OaziaGUvo8Pit23UGZ1m1LJmJUmpC2iccWJGMrbMlI0yEpsuSlWLjYjbqFDWns0bY1e6Ch7/gCcipZcWkMAsAWJWfLnnCjGBHIjxhJmLgVNJXK5MTVkN7EiA/Gaq5sxXoDBK+ZW+UNHrA7L2Ji1Zl9JFal+iiy3FeyUqlWJiIUxPHweOWzwvzrU6pUEfmBX2CUNKVcQ1HszcXfjUJnc5TOMvqRqtYqAOQKcwKUB3NFmUZdBpJZCzRkBFWI6wR1uikAhZBiKQoC5AaYR48XH4FHGyPsFFrhEUfWd4uJJI2pejlhBuaO9Da0SkZfxbTFqVU8dSjJo0GfGtD4Ce0OYHWRoknnOg5wgKpjPgIIEhXBrmxkPmOzClGAHzUwtFHmFB0z/RUpAYZXMJiYTxAD8ehmdVZPo+8UMelvv9LBTsunG88z8tMUIphOJoR1XFw8N0w1TuOopPpCVazZCUgDUc7WztkZwpLeoStKarrfyYjrEbYfLDJDmiUf1V1rBFWKAAQaqawXFFWzE5otjgr2MXd45F6WbYLE6gkOeGWdkkoGohxOJrxHDs5Di3N0siCj8YTcHGcRM9XLZ6whtMgjekVbtJwwaUrZVIGZqMWnNYFTiu+WEarR7gojFA0AJhlbnJcjJqUwOm6/ZJtPfxuHoJ5wo0tHWhn5n3H1BNmbi4cflrfZ53i74UDEj4qMxRsqN/DA03tUm+Y9YTVFooGyAirE0l7UrhCHezwBmV/3CadCVpOfNH3F+yIS1GWgEQ1K8jFvakWYKtYrRc8YbnCLDYUbdBqJP3E0UROvzforFrHccn0JEA9njAgnSkc0hOWpAx6wpyik2hGG7XGiKvAK2siL8oCvLl7jkkiOlzynnBNvXjsYhbPQa+9cK6x3pq/EWa9YCC2N4FWZiyhQ+sdZwgAtYynn6ExqqINLhiyM4VlKqTVPEdYgIywGmEvzmEKdbB3f0o9YY7jgrYpxaU9SSAc1Sz24q7RiXLo0iEOHbLtSbEMU8nlUF0tZwM/ofGERK4yKyULRq16pr/ITlIKlrtnw9HWnjAb9ZLpSYXWwojnJXelMhoANBot0piopqtFpkYDQI1TPPQglxN/N8H0o9nK6HSTPvSIzy5gZf5WOzgOreevM7Wt4vMwO1YppihiNujA/rnK9QpL1bLU8/cjQEZYjXShPQkADp4WV6n2tSsfgRisQjouQh0C4ehHSy7u+YDmwgWN1Y+W84RjKdQBeMfypUB81WD1e0U0Sj3hnmZ19W5KJymF6BWWpAx6Ic2ohcYgvumMNBTd0elBdZ24Zah/GEIdAmb2e2qWv1k6zXiQOcznITHCrf6ecOxHGPojN4zBcT7MfpaJMtmZXmk1otFwsBhD9wqrXS0LICOsTrog1NHp4XGIMcKX5inXgQ2mHx3uBKUuEU5hFusJ+7UnAdKLYUtHJ040iDWBYxkKFDBD7Om4GP1eEY4TkspoNYWiAWmbUlPIwiypEbYY9ZLK6EjlKo+ebZL0x4frCQOAhfmeAs0UrmGFOhipx2A5YWlldGyNg5zwiUPwhBl9bLsKZFGVIK2QlnrCah/eAJARVidsODqM9qSjZ5vQ0iFWYwrHCAeTrpToRsc0HB1GYZaMh+UP2ycMAEfOiD2mWFZGC5g1TEVn0CKmY9IeYZUUZQlIjTAXOGLhbvP2CftjPZ8TZsLRvcyFEa2HLcrKthgjGk1pYfKhzgA3S6fd4tfLYfLYwfqEpUIdsT3/tBotzOw4w+YzQJsLtRrxjUu2ym72AmEJIdjB8zxOUWEWERFNTNVsGDlhNhRtNxvC8vKCqWaxnnCP1HgWZgUzwmIRff/2JEBex5fNHcbDE7ZoxK/hCiZu0Zh8nnDQwizHSek2W0/oddLBDTkpkak1dbUyWkD6Pcm/J1aoI4dRmWI9NbEnLDYO2XHIVVo5VuDiHOCqkQh12K2R3QTFG7aQkvWEG1s60MZUoJMnTChDMkFJubE7cEp8wQjHCwYC60d3eDpwrlWcw4yZUAcQXmGWTJjTH51WI8kfsbnDuHjCOvEFoCnQrFqeP6+WpU6hDgHJJCW/thcJ7HdkMAMp6TjXdhIco0qVYYjsfVae6VpRloCZmTgkN9KTb3NJhDpyM4tEv8sVZgljUuMdjga84wxF62ltkJWstFvUdZ4FQioLKs4Js0VZQHw+53AhI6w2PB6A7R8No0Wpq0Y4UGHWWZlK3tgWZoWhmBUiJwxIi7PY3GF8jLDYc3QGmlXbfBZtna2oU6lQh4DEE+aC9AlLvqOeAMfhVLO4wtjTYYPbHVmRHOsJR2qELUz/s9z35Dh3WCLUkWMfJPqdNcIe3jtXGJCqtcU6HA3IjDNsd4B3nkYdqxutcqEOgVCTlNiiLLvZAINOfSZPfSvq7rScA3hxCCWccPSBU+K79oG54VWHBjLCbHuSTqNDeiyrKJUWZsnlGm1SIxxKqi4uhVms0eqU3qkD8MpVaqV9mqrzhOValAJFLGR6hAGgylEl2uxpy/YZqnDweHiJWlbERpj9ntwtkn1qZIQ6ctLFVd1yvaxCSPqMI77V0QBgZd6Xo92JZscJyc1E0hjhVDa8LjbCkh5hFeaDATLC6oMNRQNexSwFNLZ04ESD+ILR1XC0EIpjhTpiqpYFSAuzOprldYkD5BpZ2F5hlli3KAGAmf1sPVLBBgBAozQUbTVYZXuNEwnrCTcHK8xiw9HnxVSqGhkj3J6NpgiM8ImGFrR2iG9eIzbCTD2Cs1P6PZ2uPyz6PcsjFuoAvL2sTMQajS0daGpzo6ldXDwZS8lKAStz0+Rwt6DW8b1kP7XrRgtIPWEmHM2OMCQjTCiCbU9KSQd0ygzEQSYUrddyYYnXAzKFWW3ynnBMi7IAaWEW4NVTZgmQa2Rhw9EscSnMYkLsLk8AY+OQCnWoZXqSP/KecKBwtLysaLWjWrTZ0x6ZJ8yGoq0pOmRHmGIwG8Tfk5OXa30RFwPmaqSvpdHIjDNsccuqZcXFE2bOP4enFbUu8U1sGqeFSS8OxyeCPn36gOM4VFdXB9wn1KhINiesRrUsgIyw+pBIVio3dmxl9CXZ5rBzIIHC0WxldEzbkwBpOBqQv8AHyDWyyLUpCRh1GpiN0vBvtDEzNwcudEIyZw04357EVEZHKOMYSyQtSlx44Wie56WecFt20AHtgZBURudYIo7UWFLEY/+cfKdkn9NNp0W/s0IdAnK9wmyY1GzUIS0O55+FOf8cnnacZYayZDN1C2qGrY5mzxu54Q1qRN0Cod0RiVBH5EVZg8IMRQNSI+xsd4LneckEpZgKdQCA3gRwWsD/AigX6gwywtCfYDnhWEtWCrAD450cB3S0AAbG85BpT1KjJyxtUQoWjpbeLNU016CFybdGGo6uPCO+Ae0fZgTIHwsz8coFj2QfVqgjJ0U+hCtXPNTeGb/BDeK1sOMMO1HbVg/4BdqyZJS11EqoPuFkGN4AkCesPiTtSWEY4S4oZQmwRrjD04HWztb46kYDXm9WSXFWgIIflmA54XhURgOAhblxCShu0XgcJ5j5z2r0hOValHg5T7jNJf3ubAWSUDTvMYB3W6MSjo40HwxIvycnB0nEosYtbi/LTcuVPZacJ8wWZcUjFQIAVkYJy8EBte3i7yU7JcZ/11FEUpjVEqIwi8LRhCIiDEd75SrFF8CBeeHr5spqzLY5JIVZcamgVKKaJekRLpDug+A54XhdBM3MxT1gDlVGsjIZPOFOjkOrpx3oYKq+2e8IAKz5sqFoQBN2OJrn+agaYTNjrFo1GnQw39PpEEIdAnL60ZL2pDh5aFazdJzhWSbfbWdGHqoZSZSh1e3rw25zd+IsM9KVPGFCGRGGo6vPNkmqQyPxhOUqcJ3tToknHPNwNKBMNUsyo1beEw4mXxgvT5jNCTvlWno63XA7T+EMO0dYhUZYbjyjrHfPKpqlZgIGE6obq0WbPe1eLyxcT7jW2SYRauiKEbZapF6t06+AiW9rQg1z5WSFOnzHkvOEu9Aj/NRTT4HjOIwdO1b28YULF4LjOAwaNAj19eKQudUsfl8OjQa1OlaoQ5rO+eabb8BxHDIzM9He3i55XGDYsGHgOA4ffvihb9u+fftQVlaGa665Bnl5eTAYDMjLy8O0adPw73//O+T79ae6uhocx6FPnz4ApH/TnR4eGo0GHMdJZEEBwG7S4bXXXsPo0aORnp6OlJQUDBw4EAsWLIDDEUSHIMaQEVYbEYajDzL9wdkWY0TGRafRSTychrYGnGXHnanFE1aaEw5ihLPj0J4ESI1WB8ehjbm5gfMUzmg5dDI5arX1CANSTxgIUJwlqYwO3J4EIOycMOsFp+q16JmeGtYx/DHLhP5dfr3oSoQ6BOT0o7syQekXv/gFbDYbtm3bhs2bN4seW758OZYsWYLc3Fx89NFHyMgQF5hZU8S57nYNhxNMxCXbJpWsLC4uxuDBg1FfX4+PP/5Ydl3ffvstdu/ejYyMDFx//fW+7Y8++iieffZZHDx4EBkZGRg8eDDcbjfWrFmDsWPHYuXKlYrfOwvrCfvDVkYbPK2Y9sPrMX/+fOzcuRPp6ekoKipCVVUVfvWrX+Hqq6/GmTNB5nvHEDLCaiNC3Wi2KCtckQ5/2JD0UcdReBgBEVV4wq0OqUJTwMKswIY2buFouSgDG/mQGWGYqkuJrTBKhBi0BuiZoRQujcw4wwApA6lQhzcMHK4nzOqA98tOg4Zt0A0DoyENeiYH7PQbqlJzVk6oo5/sseRzwmw4Wvn5l5GRgccffxwAsGjRIt/2jRs34oEHHkBaWhrWrl3r8xb9YdsPAeA4c64FCkfPmTMHAPDOO+/IPi5sv/3222EwXPhbe/DBB/HVV1+hvr4e+/fvxxdffIEzZ87ggw8+QGpqKubPnw+nM4iGehDMKYHritmirMZPXsXWrVsxceJEVFZWorq6Gl9//TVOnz6NadOm4cCBA3jooYciWkdXISOsJng+4glK0aiMFmAFO440HhH9ruE0yDCK77JjQqjCrAC5RjmCVUfHrTBLZpyci5UolekRzkvLj0v1diRIZgprNNIbI5mUQXNHs6TNRwhHh5sTrqyJzuAGAY7jYGE6x5x+EYvT50ILdQjI6Ud3VTf60Ucfhd1ux5YtW7Blyxbs27cPt99+OzweD9577z0MGzZM9nly55+HOa8CFVzOnj3bF2pubpbKeL777ru+/fyZPn06Bg8eLNrGcRxuueUWPProo3A4HPjHP/4R+M0GQSszU1jAvyir/UwVzuzZhMLCQqxZswb9+l24YcrIyMBf/vIXFBQU4P3338fRo0cjWktXICOsJtpdgJspalE4S5jtEY4kHyzAesLfNXwn+j0rJQtajdhQxARJODrExd1kB/TyYchgOeF4ecJGrRHsKlzMUAw5T1htmtH+KJqkJDPl6qhDfLHjeS7inHA0i7IELMyl0emnnc4KdeRoAkdZ2JBpratNNE0JCL9FyWKx4Je//CUA4P/9v/+HG2+8EY2NjfjjH/+IG2+8UbJ/dXU1brnlFmTaMnHgJ/tx7E/H4HbKf8aB0kyFhYUYNWoUmpqaRDlfAPjyyy9x8OBB5OXlYfz48ZLnfv/993jhhRcwc+ZMXHfddRg9ejRGjx6N9957DwCwd+/ecN6+CDlpUEDsCTd/uxMAMHPmTFgs0hsRk8mESZMmged5bNu2LeK1RAr1CasJOclKBROUGpulcpWRVEYLsEaY9YTjEooGQoejJRd3+VA0AKTotUjRayTFa0D8PGEAsECHc7hwAXS2Noh3kDHCaswHC0jblGQKsySSlb0k+WC+Ix3gvcYs7JxwlDSj/TFzOgAXjKXL73uqaRZ78LkBhDoA6c3f8XqpDnUkk30eeughvPTSS/j0008BeI3xAw88INnP5XJhwoQJyMrKwjvvvIOn1j2Mg387gaMvH0W/Bf3A+YXtdeBgYwen+DFnzhzs2LED77zzDmbNmuXbLoSi77jjDmiYXPnbb7+NBx98EK2tAXTSAZw7dy7gY6GwBAhJ++eEO2qrAQBr1qwJWAwmeMAnTshE12IMecJqgs0H602AMfQF5QDTmmTQasKWq/SHDVuxYcO4CbyHGmcYYoQhS6Be4Xh5wgBgZnKoTe3SEPvJJJCsFJBOUmLarnhepjCrl6xcpe8YYYSjG5ulLT/9e0R+AypgYb4nR1uD7/+nW5UJdQBSI8wKpBl0GknxlhLa2tp8Xl12djaWLFkiu9+f/vQnnDp1Cv/4xz9w0003oejqHBTML0DLdy1wfimOnmVpUqDhApuEmTNnQqfTYf369b7Ka57nfR6tkDcWOHLkCO677z60trbi8ccfx5dffgmHwwGPxwOe5/H6668DADo6ZDThFRKoOMs/HO1p84bPDx8+jB07dsj+HD/uLfBsaZHeJMUaMsJqgs0HKw1FM/ng/j3M0Gsj/2rlCjj8iblQh0BIT1hZZbSAXF44Va+Ni2SggFkrvhGQzKptPCbtEVazJyyXE/a/WWo+B7BTiGw9A1ZGA4Cr/UK/ZygO14o/P52GQ2FW17WPLYwWtKvjgrdd4xZ73oGEOoDgaRDAG4oON9/f3t6OadOm4dtvv4VOp0NtbS3+7//+T3bftWvXYsKECcjL86Y0rLoUmPqZYMg1wLFH/PeUrQ9+82K32zFp0iS0t7dj9erVAIAdO3bg+++/R//+/TF8+HDR/qtWrUJHRwdmzZqF3/72txgyZAgslgtyoseOHZO8RjCE5/mfG/43MJ72C4bX3xPmDN5Iw+uvvw6e54P+lJeXh7WmaEBGWE30Gw88sA24833g1teACQsUPU0yvrALoWhAXrDDn7iFo0PmhGV0o4Mgd0GMpxcMAGatOGftahcrL3kaT0jGGCaTJywJR7NyleAAS14AoQ4vPA80t0v1muVg88F97GldugEVMOvE35PTzwgrFeoAAucsLzw3/FD0vffei82bN2PKlCn485//DAAoLy9HZ6f0M9u/fz+Ki4svrOf8rOSUniloOymOINhTQhdbCt6u0Fok/MsWZAHwDV8YNWqU7LHCzQWnpXnPtdraCx0F/p6wu+FCL3eNXwW63u79fvbt2xfW68ULMsJqwmgB8i4H+k8ChswGrrhD0dPYcHRXKqMBBUZYLeHoKHjC8Rhh6I+ZGRjv8h8Y396Mc+0NaGfaa9QoWSkQsjCLDUVbcuHRaCWFWf6eMKC8OEsyuCEK+WBAOlPYed6b59tbJEIdORnyQh2AdMgAS7hFWU8//TRWrFiBwYMH429/+xt+/OMfY8CAATh48CBWrFgh2b++vh7p6ekX1nM+1aRN06KzSWy07Qpurm+77TakpqaioqICx44d83ngckY4NdV7I1NTUyN57ODBg2FXRWdlZcFms6GlpQXffPON9/343eS49m7w/b/dfaH2w1R0DQBgxYoVOHtWrHegBsgIJzleucroVUYD8q0M/sTNCLNFIv4elscjnSUcQU44nkVZgDR86+z0K1hxSOcI6zS6+EUeIkASjmZzwjJ5+9NNp9HaKS7UYY2w0jalyhhURgMy39P5rgXnuW8lQh25AYQ6AECnDT6hKxwjvGzZMjz33HPIz8/HP//5T1itVmi1WixY4I2YPfvss3C7pZ+bf7jben5Mo1y4P1tBxMVsNuOHP/whPB4P7r//ftTW1mLIkCG49NJLJfuOHj0aAPDqq69iz549vu3ffvstZsyYIeonVgLHcSgpKQEAPPbYY3C5XL6bHNfXG+H6+hPZ56XkF2H6jBk4e/YsJk+ejC+//FL0eGdnJyoqKlBaWoq2tgAzvmMIGeEkp6quCW1uccVvV4Q6AAStkATiGY5mbibcrYD7fCiwuQ5gh62HMMJy+tHxDkezNzguj19oU2aEYa4pN2ixTKIJOUmJrWC3SvPBZr0ZBjCzliP0hKNlhNlokPA9na47INm3R4a8UIdAsLywUt3o9evXY/78+TCbzVi7di0KCi5opM+ZMwcDBgzAd999hzfffFP0vIyMDJF8pfV8yNnT7IE2jZGsDBJW90cISa9fvx6AvBcMALfeeiuuvvpq1NfX46qrrsKgQYMwePBgDBw4EGfPnvXdPITDokWLYDabsWHDBuTm5uL3D9+O43/8Mc5+9DIyJtwr+5xssxHL33zTZ4CvvPJKFBYW4uqrr8bll18Oi8WCCRMmYOXKlYprEaKJev+6CUWwIh09LEZkddG7CxWOTlhhFnDhAs+GojU6wCyv9iMgdzGMuyfM3OC4PH6VoY3JVRkNyE9SEnnCCiqj+1j7SMbSKWlTam53S1rzouYJs7Ofzw86qKkXt+tlebzKYcEI1EYDKLsJ3LNnD2bMmOGrRB46dKjoca1Wi4ULFwIAlixZIvLmiouLsX//BYUv6/kxja0nWmHMF792tlV++AnLDTfc4JPE5DhO1K7kj06nw8cff4yHH34YOTk5OHz4MBoaGnDvvffiiy++QM+ewWs45Bg4cCC2bt2K66+/HhqNBjXHqqCz5SD79mdgGTpV9jm5thSYzWasX78ef/3rX1FSUoLm5mbs3r0bdXV1uPzyy/HLX/4Sn3/+OVJS4j/kgfqEk5yDTD64q6FoIHg4mgOHrNTALRlRhS3MArwX+DS71Ahb8oEQAiJyOeG4e8LsxR2d3kokjpPvEVa5EZb1hFv8C7OkalmsJ9zX1hcnjTrUuS5EBZSEo7+rbRK1/HAcutSa54+FOccd52cKn3Z8L9qeowl9/gT1hBWcf0OGDAkp7XjnnXfizjvvlGy/6aab8PTTT+P06dPIzc2F1dQDLdUtaD/djtwZ4qpuu8I0k8FgUNzba7Va8corr+CVV16RPDZ37lzMnTtX9nlCUZccQ4cOxbp16wAA6/edwoMrdvseG/+bzfjhFfl4ZWOlb5tQ/KbRaDBnzhxJK1WiIU84yYl2ZTQQ3BPOSMmQ6AXHDH0KwHoZgpclyTWGvqtWRU6YHRjPcV6lNABwHE+q9iRAmjttZnPCMp6wnBFm86ZKwtFsKLpXRipS9NFRcmONsAtea1/TpFyoQyC4EY6t53XfffchNzcXN998M/75z39i97bDOPbqMaT2S4VlqPhaoebag0CwERRHSwdqGN1otY4wFCBPOMmJpma0QLA+4bgVZQkYrd78r0CgcHSIfDCgDk84zSQO5fvGGRotsuFoNUtWAoBJz1R7C++H5wHeI3uzVL2vWrSpj62PxAgrCUdLK6O7fgMqYGGU6lwaDry7A6fbxB5gjlF8UyVH8JxwbM8/i8WCTZs24ZFHHsEdd9wBTsshtTgVebPzRGpZgFeONtmQzhTukExQyrWp2wiTJ5zENDS34xRz1xeNcLRRa4QhgB6u3RSnfLBAoDalMHuEgQB9wnH2hC0m9uKu8d1Y8Ekm1AHIiXVwAN8JdDQDrhrv//1wpWbgTItYlKavNTJPuPKMOAoUrXwwAJiZ76mT49DSXIOaDrHhzwki1CEQqFdYp+GQGWS6V7To27cvPvzwQ7hcLnz1/VcoeKAAOqv4807n9AGHUKgZVm2so5NH9Vlx730kvdjxhIxwEsOGog1aDfrapTNeIyGQN5wQT9gfIdQZgSfMeh16LRd/sQ7m/fhG//E8HM5T3sImP9TuCbNGuEWj8SpjtzqkoWitAdWM2pSG06C3tbdkLJ2SnLCkMjpK+WAAsFikNz8O5ynUMEIduVbp/F2WQJ6w3Wzs0sjFSAiUarLronPdiDdyspXfnxNPeVJ7OJqMcBLDhqKLcromV+lPoD/WuBthtjhLCEeHqRsNePNvkwddqKC+/cpeSDXEYRqUHxZGGrBVo0FHcz3QUo+TEF/gOXDINYX2tBIJW5gFnPeGWxulalnWfFQ5xSIdPc09YdAaZDzh4HrC7W4Pjp4VX2z750TRE5bpAHA6juG0RKjjkpDHCmSEYx2KliPgzbUheFuiWpGrPGe7jHJt8f+cw4FywklMLCqjBQJVSMe9eEMuHO1uB5ziAhkl4WgA+J/SK/HxNzXQaTlMvjR4S1MsYFt6AMDVUosMmcroHqYeqg8Ryr2fJo0GtjaHTMpAvigLkA5ob2oLLlt59GwT3B7x1Taa4WitVoc0D++9oTjPqZq9UqGO7GL2qRICGuE4R2EAQK/RIxUcWiD+7Ozx6niIMjqtBmkGLZqCyJyqPRxNRjiJkVRGd1Gkwx/VeMJyqlnOUwBzEVHiCQPeP9obL09ciJcN3wKAq9lrhCX5YJW3JwFAqi4VHDjwft+HVzVLJhxt6ynbIwwAZkN44Wg2FN3DYgw4USdSzODgn12sPLtfsk+P9OBCHYA0b+l7boKMg5XToYUXRxrsCnLbasWaqg9ohNMMWkkFtdqgcHSS4u704FCN2AhHozJaIFDYKm5CHQJynjDrYelNQGpo8Xk1kKpLBRsAd7XWy44wVLNmtICG0wQY4iATjg7QngRIPeFQ4WhJZXQUQ9ECFuabOuwSv58sD2DQRd4nnAhPGACsMkWX2RZlQh1qJNjNV47KK6MBMsJJS/XZJpFIOQAMjGY4OsBYs7iHoyWFWQ3y+eAwx8ElCo7jYGYu7q7WevkRhkngCQOB2pQaJZ5wpyUP3zNiFz4jLGlRCh6OlmhGR7EoS8CiEa/pSIc4/ZMToIOAJbARTpAnzEzyAgC7LXSBmVoJpkiWR0aYiBX7mVB0jtWIzLTotTuoxxOWCUfL6BEnE2ZG7MTZ1ijfI5wEnjAgDbH7eoWZiMXJlDS0e8TFZ0I4mr2QhmpRipVmtD8Wxsge0Ypv9HJ0ytI/gVqUEuYJM5O8AMBuTu5wdCDUng8GyAgnLWxldDSLsgD5nLDNaINRG+cLh2w4OvzKaDVhZgfGtztlJygliycsnaTEAU21QJO4H7iKE3u3VoMVmSlesYs0o/KccKeHx5FasRG+JAZG2KwVX8DZEZO5KaGFOoDA4dJEVEcDF8YZ+hP3Wo8oEmxcpNrbkwAywknLwQQY4YT8obIeuVzVbbIZYZ34wuDsaEJz43E0aJnhDSoX6hCQnSlce1CyX1WnWEShr62vb8xeOC1KJ+pbJJPDoqmWJWAJ0TubY1JWXZ+i18Kok15qExaOlmmrinuEK4oE84TVrpYFkBFOWmJZGQ3IG+GE/KHKecIR9AirCQsTDnR1NOEUoyIFqF+oQ4BtU2rWcMAZZuSfwYzqZvFwdyEUDUjD0a0dHrg7xYZW4HCt+Ny3pephN0dfecoi0wPtT24YeVQ2L8xxiMmalWC1iYuwUrUpsv3eyULQwizyhIlYUN/ULtFHjWZlNCCfE1aFJ9zamPw5YTaH2nIWJ5l8Y6YxHak6aQGNGpH1hOWmJznkK6MBaTgaCFycJZcP5mJQmGcOMk0MAHIy+is+FmuEs9IM0EVJWCdc2Btsuyk7Jp9fvAjUAgZQOJqIEQcYkQ6DLnpylQJyYh1x140GpIVZng7xlB4AsCVXewV7cXd52iWV0Xnm5LmxkLYoyVxWbPIjDAXYcDQAOAOEpCtr2MEN0c8HA4CF7VFnyLFfqvhYbMg0O0GhaADox/Q2909XfjOhRoJ5whSOJmICG4oekGOO+l21XDi6R2oPmT1jjNxMYRZrcuROBdiLu0ujkVRGJ0tRFiDjCct4VY2WHJxrFU8g6mPrc+EYBqkRDlQhfbg29pXRAGBJCd573hVPOFGV0QAwIncEJvWe5F1Hag88cPkDCVtLMHbt2oWpU6ciIyMDaWlpGDFiBFauXCnZL2BOuKURy5a+hOnTp6NvX2/9gRo9flLMSkIkldG50Q1FAwFywonwhIOMVQQAmLIAg7TlQs2kpaSLfndqNJLK6GRpTwICtCgxVKeaAb8Aho7TocBPIEKj4WA26kSGV26cIc/zknB0LCqjAcCSGrj6OVOhUIeAmoywhtPgpfEvob6tHiadCSk69XmLFRUVKCkpgcFgwKxZs2Cz2bB69WqUlpaiuroaTz31lG/fQJ6wqekUFjz9NDiOQ1FREUwmE5qbm2X3TSTkCSchsdSMFjDpTdByYu8sITlhnQEIdpFIsnwwAFiY1haXjBFOZk9YLhxdxXj6vSy9oGf6pdOM4n3k2pTOONsk22MVjjYHEabJVSjUITC4pzj6MbR3YhXeOI5DZkqmKg2w2+3GvHnzwHEctm7ditdffx2//e1vsXfvXhQXF6OsrAyVlZW+/QOJdRRcMgBbtmxBY2MjDh06hIICdaatyAgnGe5OD75lcmID86LfnqHhNBiWM8z3u8VgwaCsQVF/HUUE84aTLB8MAGYmouDScDjFhqOTpD0JkPOEpSG/amZClH8o2nccBTOFWS84Va9Fvi02BWxWU+D0S44uPMM/c3gBbrw8D1lpBtw2tCduG5p8N4/xYtOmTThy5AjmzJmDoUOH+rZbLBYsXLgQbrcby5cv920PFI7u0ysPY8eOhcUS/etjNKFwdJLxXZ1UrjLaldECi0Ytwm92/QbODifmXzE/cdW6KTaJ8IMPW/JdzFgPq16rRT3jPSaTJyxpUeJkPOEOcR2Df1GW7zhMWFEuHC0NRafFbCavOYiKlFKhDt+xjDr8cc6VEa/F4+FR39weekeVkGEyRPy9VFRUAACmTJkieUzYtmXLFt+2QGIdeTG6OYs2ZISTDDYfnGdLQbopNv2GvSy98Pvrfh+TY4cF2yvsT5L1CAOAhfHsz2mlM42TpUcYAExs37PMxbeqRdwj3NcqY4QVhKMrz4iNeSxEOgQsQb6DnDjPea5vbsewJf+K62t2hS8WTEKWObK8txBqLioqkjyWkZEBu93OhKPlPeFk6BEGKByddMRapEOVBAtHJ2FOWG6coehxXWrAUZJqhPWEmzQa0aDJjtRMHGMmEMl6whGEo2NVGQ0AKQYzdOyE+PPkWHvH7HW7O42N3go+m02+M8Jqtfr2Abwtmql66Y1sri1xxW/hQEY4yYi1ZrQqCeoJJ19OWK4H25+8JMoHA9LCrE6OQ6tfK8iJ9Fy4PWKD6q+WJWA2ij0al4wnfPiMWPrykhhMTxLgOA4WeRuM3DDak4jYIyfYQZ4wERPiURmtOoL1CidjTjiEJ5xvSa4Qu9z7afILSVeZxfnTzJRMpDNtWoC0yrWpXWyEG5rbUedqE22LxRxhf8wBLpHhCHUQ4SF4wP7erj8Oh0PiJcu1KSWDWhZAOeGk4lxTO2oc4ovQpTGojFYdgcLRnBZIwhFsJr0JHIAATlZSFWUBUk8YAFycBnZ4CwirDSmAnz2V84KB0C1KbChar+VQmBnbHnELpwMgVe7KyZTmK2NJhsmALxZMiutrdoWMLtSpCLngyspKDBs2TPRYfX096urqMGrUKNF2uQrpZFDLApLcCO/atQtlZWXYuXMn2tvbUVxcjEcffRRz5sxR9Pzt27djzZo1qKioQHV1NZqamtCnTx/ccsstePLJJ5Genh7bNxAmbCjaqNOgT1byCq8rJpAnbMkDtMl3Cms4DdKghQvy2sjJ1J4EAAatAQaNQTQrWOQJa8W3G3L5YEAmHN0W3Aj3yUqLuf6yRaMHeLERDleoIxpoNFzEhU7Jxrhx4/D8889jw4YNmDVrluixDRs2+Pbxh42iWFJ0MMmosKmRpA1HV1RUYPTo0di2bRumT5+O+fPno66uDqWlpXjuuecUHWP69On4/e9/D4vFgh//+Mf4yU9+ApPJhBdffBFXXXUVzpwJ0BaTIFgj/INcS8JE4ONKIE84CSujBcyawHq3yVQZLSBXnCVQ7REPGwlohNlwNGOEKxkjHOtQNABYNFLDlxOmUAcRHhMnTkS/fv2wcuVK7Nmzx7fd6XRi8eLF0Ol0mDt3rm97XV0d3GePo7P5Qvg6WULRQJJ6wqyiitDQXVZWhmuuuQZlZWWYMWOGbIm7Pz/72c/w4x//GHl5Fy56PM/joYcewv/8z/9g0aJF+OMf/xjT9xIO3bIyGghcmJWE+WABs8YAMMZJINk8YcDbpnQOF7Sh/aUrq9oYzegA4WgLUx0dKhzdP4ZFWQJmXSrQWS/alhumUAcRHjqdDsuWLUNJSQnGjBmD2bNnw2q1YvXq1aiqqsKSJUswYMAA3/5Lly7FXxctgu3a2UgfXQrgQija31ifOnVKsu23v/0t7PbEzlJOSjcqXEWVQPzyl78UGWDAWxG5cOFCAOKGcDXQLSujgcDh6CT2hC1B5AIvDk/YG46u12jQ4BZXNAfyhNlxhqHC0bHSjPaHnf0MADnGxEpOdgcmTJiA7du3Y/To0Vi1ahVeffVVZGVlYcWKFXj66adDPl+YKvf222/7fhwOh2Sby+UKdpi4kJSecLiKKuGi13tDhTqdej6ejk6P5CLUbYxwoHC0NXmNsFknn8s3avTISsmK82q6jnSSkvf+vlovDrvrNfqAhWfB+oSb29040dAiejyWQh0CFoMFEN9DIDct+YoBk5ERI0Zg3bp1IfcrLy/H/Y/+Ere9ugM1jjZYU3SYM9Lbx80H6PNWE+qxMmEQrqJKuLz55psA5I28P21tbWhru1CtLNxpxYLvapvQ3imWq4zF9CRVEjAcncRGWKaiGADyUnuoctxaKNg2JSEnXGURh/p6W3pDp5G/7EhalNrc4HkeHMfhCNMfzHFAv+zYFyVaZERTSKhDfeSnp+LjR8fim5MOFOWY0SOB85rDJSnD0eEqqoTDnj17sGjRIvTo0QNPPPFE0H2ff/552Gw2308sp3Swoeh8WwpspsDFPRcVAQuzkjgnHECwI9+afOIjgNwkJe+NRJVJ/D4DhaIBaTi6o5NH23md9MO14nqIggwTUmRUkqKNWaafOTf9kpi/LhE+6SYDru1vTyoDDCSpEY4VVVVVuOmmm9DZ2Yl33303ZML+ySefRGNjo+/n2LFjMVvbge4o0iEQMCecnAYLAMxG+feUZ07OG4tAM4XZcLTc9CTfMYxSD1kISbOpmFiNL2SxpEjzvznZxXF5baJ7kJTh6EgUVUJx9OhRTJgwAbW1tXj//fcxYcKEkM8xGo0wGuPTuyepjO4OIh0Ccp6wLhVITd4CGYuMhwUkn1CHgMQTPp8TruLExVXBPGG5ubCuVjfsZiMqmfGdsdSMFq0pLUeyLd5CHcTFTVJ6wv6KKiyCokqo9iR/qqurMX78eJw8eRKrVq3CTTfdFLW1RouD3bUyGvAKcrA5VFsvb2IwSTGnyhdf5aUlX2U0IFOYpeHQAeB4Z7Nou9z0JAGjTgMdM4HJ5wnXxr8yGgD69p0EjV9tT3+NKe5CHcTFTVIaYUEtRVBP8SeQokogBAN84sQJvPfee7jllluit9AocdbVhjNOVq6yGxlhQFqclcT5YAAwp8qnOpLVE5YT6zim16GTEecMFo7mOE62Tand7cHRs2JjHq9wdLY5Fz8tvgcacEjXpODn434dl9clug9JaYQjUVQ5ePAg6urqRMfxN8Dvvvsubrvttji9g/BgQ9Ep+m4iV+kPG5JO4spoALAE8ISTUagDkPeEq5h8sD3VHnKClKRNqdWN6rNN6PSIjXm8PGEAuG/4z/CfO7/AptJ/49re4+P2ukT3IClzwpEoqixatAhlZWUoLy/3bR8/fjyOHj2Kq6++Gl999RW++uoryWv5758o2MlJP8ixQCszOP2ihvWEk7hHGJCvjtZxGmSbshOwmq4j16JUZRCHbYPlgwXkJimxRVk5VqPs1JxYotd2k04EIu4kpREGLiiqlJWVYdWqVb4BDosXL0ZpaamiYxw9ehQA8Omnn+LTTz+V3UcNRnh/d84HC+QUA8d3Xfg9f2jgfZMANnwLADmp2QF7aNWOXGFWVX4x0HKhYyCQXKXoODLSleea2kXb4lWURRDxIDn/4s8TjqKKnDFNBjUVoBtrRvtz7SPAsc+BM/uBy+8AiiYnekVdQm4Gb54liVuuWE/YaEJ1WobICCvxhOVUsySDG+KglEUQ8SKpjXB3wCtXKTbC3dITzuwH/GQn4OkENLEXaYg1crnRZC3KAqSecEtnG440HhFtU2SEU6Q54URoRhNEvEjKwqzuxJFaFzo6xR77wO4iVynHRWCAAanRApK3PQmQfz9NHWKpSSXhaHaSkqO1A98x7UnxmJ5EEPGCjLDKYeUqe6andh+5yosYnUaHVF2qaFsye8JyOW5/jFqjopsMNid88JTTJ10pEI85wgQRL8gIq5yDp9hQNOXDLhZyTGI1pkJrYYJW0nVSdangELhiv9BaCK2CKAabE/76hFgVL92kR1aaIbJFEoQKISOsctjK6G4dir7ImDVwlu//l2VdhqE9krfiW8NpZEPSAkpC0YC0Ramlo1P0e/9sc1JOmSLCZ9euXZg6dSoyMjKQlpaGESNGYOXKlYqfX1FRgTlz5uDSSy9Feno6TCYTfvCDH+Cee+7BoUOHYrjy8KDCLJXDVkZ3y6Ksi5TSS0sx2D4YdS11GNNzDDRcct8Tp+nT4OqQH5KupCgLkB/i4A+ForsHFRUVKCkpgcFgwKxZs2Cz2bB69WqUlpaiuroaTz31VMhj/Otf/8L27dsxcuRI37EOHDiA//3f/8XKlSuxbt06RTMCYg0ZYRVT62xDnYuVq6Rw9MXE5dmXJ3oJUSOYJ6zUCLM5YZZLqCjrosftdmPevHngOA5bt27F0KHeCFFZWRmuueYalJWVYcaMGSHnAyxYsABLliyRbN+4cSMmTZqEJ554Art27ZJ5ZnxJ7lvvixxWKStFr0Fhd5OrJJIGud5ngWCa0aJjyExS8oeEOi5+Nm3ahCNHjmDOnDk+AwwAFosFCxcuhNvtxvLly0MeJyVFfq7wxIkTkZGRgcOHD0dtzV2BPGEVw1ZG/yDX2v3kKomkIagnHGR6kj9sixJLUU43jQR5PEDLuUSvQjmpmYAmMh+voqICADBlyhTJY8K2LVu2RLy0nTt3or6+HqNHj474GNGEjLCKYSujB1EomlAxgdqUckw5MOlNio4RLBxtMmiRb5P3bi56Ws4Bv7kk0atQzi+OAGnyk8JCIYyolQs3Z2RkwG63y46xDURFRQUqKirQ1taGyspKrF27Fna7HS+//HJE64s2ZIRVDFVGE8lEIE9YaSgaCF6YdQlVRncLGhu9bWk2m032cavViuPHjys+XkVFBRYtWuT7vX///nj33XcxbNiwri00SlBOWKW0uz04wigFUWU0oWYC5YSVhqIBaYuSP/GaIUxcXJSXl4PnebhcLnz++ecYOHAgrr322rDanWIJGWGVIitXSeFoQsUE8oSVVkYDwcPRpBndPRA8YMEjZnE4HAG95GCkpaVh+PDhWLNmDQYOHIj7778ftbW1XVprNKBwtEqRk6uM9wxVggiHaISj9VoNjDqNRKoS6OaV0amZ3jxrspCaGfFThVxwZWWlJGRcX1+Puro6jBo1KuLj63Q6TJgwAXv37sV//vMf3HDDDREfKxqQEVYprBGmUDShdgIZ4X62fmEdx5KiQ5urXbK9W4ejNZqIC52SjXHjxuH555/Hhg0bMGvWLNFjGzZs8O3TFU6ePAnAa5ATDYWjVcrB01QZTSQXcjnhVF0qeph6hHccmZC0QatB70xlFdZEcjNx4kT069cPK1euxJ49e3zbnU4nFi9eDJ1Oh7lz5/q219XV4eDBg6irqxMdZ+vWrbIz4zds2IA1a9bAZrN1yaOOFom/DSBkYT3hgeQJEypHrkWpj7VP2HKccnnhPnYTdFryGboDOp0Oy5YtQ0lJCcaMGYPZs2fDarVi9erVqKqqwpIlSzBgwADf/kuXLsWiRYtQVlaG8vJy3/abb74Zdrsdw4cPR0FBAVpaWvDVV19h69at0Ov1WLZsGdLSEi9+REZYhZxxtqKOCcdROJpQO3Lh6HDywQJynnBRD4oEdScmTJiA7du3o6ysDKtWrUJ7ezuKi4uxePFilJaWKjrGokWLsH79emzfvh21tbXgOA4FBQWYN28eHn30URQXF8f4XSiDjLAKYUU6UvVaFFIojlA5cuHocNqTBOTalKgyuvsxYsQIrFu3LuR+5eXlIg9Y4JFHHsEjjzwSg5VFF4rvqBCpXKUFGpKrJFSOnCpWOO1JAnKecLeujCYuasgIqxCqjCaSEVlPOAIjLJcT7taV0cRFDRlhFUKV0UQykm5MR6G10Pd7D1OPsNuTAOkkJQ0H9LUnvoCGIGIBGWGV0ebuxOEzYrlKqowmkgGO4/DrMb/GlT2uxOXZl+PXY34NvTZ8gRl2klJBpgkpem20lkkQqoIKs1TG4TMuuD2MXGUuecJEclBsL8bbN7zdpWMUMEWIg3uGL1FIEMkCecIqg62MLshMhYXkKoluxORBORjaOx0AYDcbMH98Eo3wI4gwIU9YZUhEOmh8IdHNMBl0WPXANTh2rhnZFiPdhBIXNWSEVcaB01QZTRB6rQb9sqkimrj4oXC0iuB5HgdOUWU0QRBEd4GMsIqodbbhXJNYrpLC0QRBEBcvZIRVxH4mH5xm0NLkGIIgiIsYMsIq4rvaJtHvJFdJEARxcUOFWSrintF9cfOQfBw45cDBU06km6gqlCAI4mKGjLDKsJuNGFOUjTFF2YleCkEQBBFjKBxNEARBqI5du3Zh6tSpyMjIQFpaGkaMGIGVK1cqfn5FRQU4jgv48+mnn8Zw9cohT5ggCIJQFRUVFSgpKYHBYMCsWbNgs9mwevVqlJaWorq6Gk899ZTiY40bNw7jx4+XbO/Vq1cUVxw5ZIQJgiAI1eB2uzFv3jxwHIetW7di6NChAICysjJcc801KCsrw4wZM1BUVKToeOPHj0d5eXkMV9w1yAgTBEGoHA/vQUNbQ6KXoZh0Yzo0XGTZzk2bNuHIkSO4++67fQYYACwWCxYuXIhZs2Zh+fLleO6556K13IRCRpggCELlNLQ1YNx74xK9DMVsuWMLMlMyI3puRUUFAGDKlCmSx4RtW7ZsUXy8yspKvPLKK2hubkZhYSEmT54Mu90e0dpiARlhgiAIQjVUVlYCgGy4OSMjA3a73bePElauXCkq6EpNTcWiRYvwi1/8ouuLjQJUHU0QBEGohsbGRgCAzSY/R9pqtfr2CUZ2djZ+85vf4MCBA2hqasKJEyewYsUKZGZm4oknnsCf/vSnqK47UsgTJgiCIC46iouLUVxc7PvdZDKhtLQUV1xxBYYNG4aysjLcd9990GgS64uSESYIglA56cZ0bLlDeR400aQb0yN+ruABB/J2HQ5HQC9ZCZdddhlGjhyJbdu24fDhwxgwYEDEx4oGZIQJgiBUjobTRFzolGwIueDKykoMGzZM9Fh9fT3q6uowatSoLr2GUJjV3NzcpeNEA8oJEwRBEKph3DhvFfiGDRskjwnbhH0iwe12Y/fu3eA4Dr179474ONGCjDBBEAShGiZOnIh+/fph5cqV2LNnj2+70+nE4sWLodPpMHfuXN/2uro6HDx4EHV1daLj7Ny5EzzPi7a53W784he/wNGjR1FSUoLMzMRHFygcTRAEQagGnU6HZcuWoaSkBGPGjMHs2bNhtVqxevVqVFVVYcmSJaI87tKlS7Fo0SKUlZWJlLFmz54NjuMwatQo9OzZEw0NDdi6dSsOHTqE3r1747XXXkvAu5NCRpggCIJQFRMmTMD27dtRVlaGVatWob29HcXFxVi8eDFKS0sVHWP+/PlYv349KioqUFdXB51Oh/79++Ppp5/G448/joyMjBi/C2VwPOuvExEjVO01NjbCarUmejkEQRBEglBqDygnTBAEQRAJgowwQRAEQSQIMsIEQRAEkSDICBMEQRBEgiAjTBAEQRAJgowwQRAEQSQIMsIEQRAEkSDICBMEQRBEgiAjTBAEQRAJgowwQRAEQSQIMsIEQRAEkSDICBMEQRBEgiAjTBAEQRAJgowwQRAEQSSIpDbCu3btwtSpU5GRkYG0tDSMGDECK1euDOsYHo8HS5cuxeWXX47U1FRkZ2dj5syZqKysjNGqCYIgCMJL0hrhiooKjB49Gtu2bcP06dMxf/581NXVobS0FM8995zi4zz44IN4+OGH0dnZiYcffhhTp07Fhx9+iOHDh2P//v0xfAcEQRBEd4fjeZ5P9CLCxe12Y+DAgTh+/Dh27tyJoUOHAgCcTieuueYaHDp0CPv370dRUVHQ42zevBnXXXcdxowZg08++QRGoxEAsHHjRkyePBljxozBli1bFK9L6RBngiAI4uJGqT1ISk9406ZNOHLkCObMmeMzwABgsViwcOFCuN1uLF++PORxXn/9dQDAkiVLfAYYACZOnIiSkhJs3boV3377bfTfAEEQBEEgSY1wRUUFAGDKlCmSx4RtSjzYiooKpKWl4dprr5U8VlJSovg4BEEQBBEJukQvIBKEoim5cHNGRgbsdnvIwqqmpiacOnUKl112GbRareRx4djBjtPW1oa2tjbf742NjQC8YQiCIAii+yLYgVAZ36Q0woKxs9lsso9brVYcP368y8fw30+O559/HosWLZJsLygoCPraBEEQRPfA6XQGtDNAkhphtfDkk0/iscce8/3u8Xhw7tw5ZGVlgeO4iI/rcDhQUFCAY8eOUYFXDKDPN7bQ5xtb6PONLdH6fHmeh9PpRH5+ftD9ktIIC3cVgbxUoSqtq8fw308Oo9EoKugCgPT09KCvGw5Wq5X+yGIIfb6xhT7f2EKfb2yJxucbyg4BSVqYFSxfW19fj7q6upDtSWlpacjLy0NVVRU6OzsljwfLOxMEQRBENEhKIzxu3DgAwIYNGySPCduEfUIdp6mpCTt27JA89vHHHys+DkEQBEFEQlIa4YkTJ6Jfv35YuXIl9uzZ49vudDqxePFi6HQ6zJ0717e9rq4OBw8eRF1dneg4999/PwBgwYIFaG9v923fuHEjPv74Y4wdOxYDBgyI6XuRw2g0oqysTBLqJqIDfb6xhT7f2EKfb2yJ9+eblIpZgFftqqSkBEajEbNnz4bVasXq1atRVVWFJUuW4Omnn/btW15ejkWLFqGsrAzl5eWi49x3331YtmwZBg0ahBtvvBE1NTV47733kJKSgn//+98YNGhQnN8ZQRAE0V1ISk8YACZMmIDt27dj9OjRWLVqFV599VVkZWVhxYoVIgMcij/96U945ZVXwHEcXnnlFfzzn//ED3/4Q3z++edkgAmCIIiYkrSeMEEQBEEkO0nrCRMEQRBEskNGmCAIgiASBBlhFbFr1y5MnToVGRkZSEtLw4gRI7By5cpEL+uioE+fPuA4TvbnwQcfTPTykoYVK1bggQcewFVXXQWj0QiO4/DWW28F3N/hcOCxxx5DYWEhjEYjCgsL8dhjj5G+egDC+XzLy8sDntMpKSnxXXgScOLECfzud7/DlClT0Lt3bxgMBuTm5uL222/HZ599JvuceJy/SamYdTFSUVGBkpISGAwGzJo1CzabDatXr0ZpaSmqq6vx1FNPJXqJSY/NZsOjjz4q2X7VVVfFfzFJyoIFC3D06FHY7Xbk5eXh6NGjAfdtamrCuHHjsGfPHkyePBmzZ8/G3r178fLLL2Pz5s3Yvn070tLS4rh69RPO5ytw1113oU+fPqJtOh1d2ln+8Ic/4Ne//jUuueQSTJ48GT169EBlZSU++OADfPDBB3jnnXcwc+ZM3/5xO395IuF0dHTwl1xyCW80Gvndu3f7tjscDr64uJjX6XT8t99+m8AVJj+FhYV8YWFhopeR9HzyySd8dXU1z/M8//zzz/MA+OXLl8vu+8wzz/AA+CeeeEJ2+zPPPBPr5SYd4Xy+ZWVlPAB+8+bN8VtgEvP+++/zW7dulWzfunUrr9fr+czMTL61tdW3PV7nL4WjVcCmTZtw5MgRzJkzB0OHDvVtt1gsWLhwIdxuN5YvX57AFRKEl0mTJqGwsDDkfjzPY9myZTCbzXjmmWdEjz355JPIyMjAG2+8EXLMW3dD6edLhM+0adMwZswYyfYxY8ZgwoQJOHfuHL7++msA8T1/KWahAioqKgAAU6ZMkTwmbNuyZUs8l3RR0tbWhrfffhsnTpxARkYGRo0ahSuuuCLRy7ooqaysxMmTJ1FSUiIJ2aWkpGDs2LH4+9//jsOHD5M+exfZtm0bPv/8c2i1WgwcOBCTJk0iNa0w0ev1AC6E8eN5/pIRVgHBhkVkZGTAbrfLDqsgwuP06dMiOVMAuP766/GXv/wFdrs9MYu6SAk1AMV/CAsZ4a7Bemp5eXl4++23MXny5AStKLn4/vvv8a9//Qu5ubkYPHgwgPievxSOVgHCOMVAY6+sVmvAkYuEMu655x5UVFSgtrYWDocDn376KW644QasX78eN998M4VFo4ySc9p/PyJ8hgwZgrfffhvV1dVoaWlBZWUlFi9ejIaGBtx8883Yu3dvopeoejo6OvCjH/0IbW1tePHFF6HVagHE9/wlT5joFrDewsiRI7F27VqMGzcO27dvx0cffYQbb7wxQasjiPC59dZbRb/3798fCxYsQE5ODu6//34sWbIEf/vb3xKzuCTA4/HgnnvuwdatW3HffffhRz/6UULWQZ6wChDutgLdVTkcDkXDoYnw0Gg0uPvuuwFAdpwlETlKzmn//Yjocdddd0Gn09E5HQSe53HfffdhxYoVuPPOO/Haa6+JHo/n+UtGWAX45xdY6uvrUVdXR3mzGCHkgpubmxO8kouLYOe0/3Y6r6OPwWCAxWKhczoAHo8H9957L958803Mnj0bb731FjQasSmM5/lLRlgFjBs3DgCwYcMGyWPCNmEfIroISjms2AHRNYqKipCfn48dO3agqalJ9Fhrayu2bt2K/Px89O/fP0ErvHiprKxEfX09ndMyeDwezJs3D8uXL8cdd9yBv/zlL748sD/xPH/JCKuAiRMnol+/fli5ciX27Nnj2+50OrF48WLodDpJVS+hnP3796OhoUGyffv27XjppZdgNBoxbdq0+C/sIobjOMybNw8ulwvPPvus6LHnn38e9fX1mDdvHjiOS9AKkxun04mvvvpKsr2+vh733nsvAGD27NnxXpaqETzg5cuXY8aMGVixYoWsAQbie/7SKEOVsHnzZpSUlMBoNGL27NmwWq1YvXo1qqqqsGTJkrBmJBNiysvL8eKLL2LixIno06cPjEYj9u3bhw0bNkCj0eC1117DvHnzEr3MpGDZsmXYvn07AODrr7/G7t27ce211/o8gltvvdVXMNTU1ITRo0f7ZP+GDRuGvXv3Yt26dRgyZAjJB626MgAACnFJREFUVsqg9POtrq5G3759cdVVV2Hw4MHo0aMHTpw4gXXr1uHs2bOYPHky1q5dC4PBkMi3oyrKy8uxaNEimM1mPPLII7LSnrfeeiuGDBkCII7nb1R0t4io8Nlnn/HXX389b7PZ+NTUVP6qq67iV6xYkehlJT0VFRX8zJkz+f79+/MWi4XX6/V8r169+FmzZvGfffZZopeXVNx11108gIA/ZWVlov0bGhr4n/3sZ3xBQQGv1+v5goIC/mc/+xnf0NCQmDegcpR+vo2NjfxDDz3EDxs2jLfb7bxOp+NtNhs/evRo/rXXXuPdbndi34gKCfXZQkYiNB7nL3nCBEEQBJEgKCdMEARBEAmCjDBBEARBJAgywgRBEASRIMgIEwRBEESCICNMEARBEAmCjDBBEARBJAgywgRBEASRIMgIEwRBEESCICNMEARBEAmCjDBBJIC33noLHMeB4zhUV1cnejmqpaKiwvc5VVRUJHo5BBF1yAgTBEEQRIIgI0wQKmPu3LngOO6inQdbXV3t827feuutRC+HIBKKdJYTQRAxZ+7cuTQjWgHjx48HzZghLmbIEyYIgiCIBEFGmCAIgiASBBlhgkgActXR5eXl4DgOb7/9NgDg6NGjvn38f+Rwu9144403MHXqVOTn58NoNMJut2Ps2LH43e9+h9bW1oBrGT9+PDiOw/jx4wEAlZWV+OlPf4qioiKYTCZJBfepU6fw6quvYvr06SgqKkJaWhqMRiN69uyJW265Be+99x48Ho/sa3Ech759+/p+v/vuuyXvr7y83Pe40upol8uFF154Addccw0yMzNhNBrRq1cvTJ8+HWvXrg34PLn3f+LECTz22GPo378/UlNTkZWVhZKSEqxbty7ocQgiIniCIOLO8uXLeQA8AL6qqorneZ4vKyvzbQv2w3L48GF+0KBBQZ9TVFTEf/vtt7JrGTduHA+AHzduHP/BBx/waWlpkucLa3S73bxGowm5xsmTJ/NOp1PyWkreX1lZmW//zZs3+7Zv3rxZdv27d+/m8/Pzgx5z2rRpfEtLS8j3v23bNj4rKyvgcX7zm98E/lIJIgKoMIsgVMJPfvITTJ8+HQsWLMDf//535Ofn4+OPPw76nFOnTuHaa69FTU0NLBYL7r//fkyaNAk5OTlobGzEhg0b8Pvf/x6VlZW4/vrrsXv3bthsNtljff/997jzzjthMpmwcOFCjBkzBlqtFrt27YLZbAYAX5HUddddhxtuuAGDBw9GdnY2nE4nvvvuO7z++uvYuXMnPvnkEzz00EM+r17g66+/xsmTJ1FSUgIAWLJkCW655RbRPj169FD8mZ04cQITJ05EfX09OI7D3LlzMWvWLGRlZWH//v347//+b+zduxerV6/GXXfdhffeey/oZ3nbbbdBq9XihRdewOjRo2EwGLB9+3Y8++yzaGhowJNPPokbbrgBxcXFitdIEEFJ9F0AQXRH5DxhgbvuuosHwBcWFoY8zk033cQD4AsKCvgjR47I7rN7926fd7tgwQLJ44InCIDPz8/njx49GvD1PB4PX1lZGXRNzzzzDA+A5zhO1vuuqqryvd7y5cuDHiuUJzx9+nTf48uWLZM83trayk+YMMG3z0cffSTZx//9FxYW8sePH5fss23bNp7jOB4A/1//9V9B10wQ4UA5YYJIUvbt2+fLdy5duhT9+vWT3W/o0KF46KGHAABvvvlm0GO+8MIL6N27d8DHOY5D//79gx7jmWeegd1uB8/z+PDDD4Pu2xVOnTqFNWvWAABKSkpw7733SvYxGo148803odN5g35Lly4Nesw//OEP6Nmzp2T76NGjMXLkSADAtm3burp0gvBBRpggkpS///3vAACTyYQbb7wx6L5jx44FAJw8eRLHjh2T3cdgMGDGjBlhrcHj8eDkyZM4dOgQ9u3bh3379uHAgQPo1asXAGDv3r1hHS8cNm/ejM7OTgCQNcACffr0weTJkwF4C72E57Ckp6cH/RyHDRsGAPjuu+8iXTJBSKCcMEEkKf/5z38AAM3NzT5PTwmnT59GQUGBZHtRURFSUlJCPp/nefz1r3/FG2+8gc8++wwtLS0B962rq1O8rnDZt2+f7/+ClxqIkSNHYt26dWhubsZ3332HoqIiyT5FRUXQaAL7JZmZmQAAp9MZ4YoJQgoZYYJIUs6cORPR85qbm2W3Z2RkhHxua2srpk2bprhdJ5iB7irnzp3z/T8nJyfovrm5ubLP88dkMgU9hmCgA7VfEUQkkBEmiCRFCKv27ds3rNyrf5+uP1qtNuRzf/WrX/kM8Lhx4/DQQw/hyiuvRG5uLlJTU32GauzYsdi2bZtqJCfVsg6CYCEjTBBJSlZWFgCgpqYGAwcODCskHQk8z2PZsmUAvIVKmzZtChi+ra+vj+lagAvhYcD7GQQrKKupqZF9HkEkGirMIgi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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "r = 3.9\n", + "xs_01 = iterate_map(x0=0.1, r=r, n=20)\n", + "xs_03 = iterate_map(x0=0.3, r=r, n=20)\n", + "xs_05 = iterate_map(x0=0.4, r=r, n=20)\n", + "with plot_style(figsize=(5, 5), titlesize=20):\n", + " plt.plot(xs_01, lw=3, label=0.1)\n", + " plt.plot(xs_03, lw=3, label=0.3)\n", + " plt.plot(xs_05, lw=3, label=0.5)\n", + " plt.ylim(0, 1)\n", + " plt.xticks([0, 5, 10, 15, 20])\n", + " plt.xlabel('iteration')\n", + " plt.ylabel('x')\n", + " plt.title(f'r = {r}')\n", + " plt.legend(title='$x_0$ value', fontsize=14, title_fontsize=16, frameon=False)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "78d8e347", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "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": "3.11.3" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/profiling.pptx b/profiling.pptx new file mode 100644 index 0000000..a692be3 Binary files /dev/null and b/profiling.pptx differ diff --git a/testing_part1.pptx b/testing_part1.pptx new file mode 100644 index 0000000..9be2747 Binary files /dev/null and b/testing_part1.pptx differ diff --git a/testing_part2.pptx b/testing_part2.pptx new file mode 100644 index 0000000..138573e Binary files /dev/null and b/testing_part2.pptx differ diff --git a/testing_project/LICENSE.txt b/testing_project/LICENSE.txt new file mode 100644 index 0000000..4b780a7 --- /dev/null +++ b/testing_project/LICENSE.txt @@ -0,0 +1,6 @@ +The material in this repository is released under the +CC Attribution-Share Alike 4.0 International +license. + +Full license text available at +https://creativecommons.org/licenses/by-sa/4.0/ diff --git a/testing_project/README.md b/testing_project/README.md new file mode 100644 index 0000000..b2c46d2 --- /dev/null +++ b/testing_project/README.md @@ -0,0 +1 @@ +# Testing Project diff --git a/testing_project/demos/conftest_example.py b/testing_project/demos/conftest_example.py new file mode 100644 index 0000000..4069350 --- /dev/null +++ b/testing_project/demos/conftest_example.py @@ -0,0 +1,28 @@ +import numpy as np +import pytest + + +# add a commandline option to pytest +def pytest_addoption(parser): + """Add random seed option to py.test. + """ + parser.addoption('--seed', dest='seed', type=int, action='store', + help='set random seed') + + +# configure pytest to automatically set the rnd seed if not passed on CLI +def pytest_configure(config): + seed = config.getvalue("seed") + # if seed was not set by the user, we set one now + if seed is None or seed == ('NO', 'DEFAULT'): + config.option.seed = int(np.random.randint(2 ** 31 - 1)) + + +def pytest_report_header(config): + return f'Using random seed: {config.option.seed}' + + +@pytest.fixture +def random_state(request): + random_state = np.random.RandomState(request.config.option.seed) + return random_state diff --git a/testing_project/demos/test_parametrize.py b/testing_project/demos/test_parametrize.py new file mode 100644 index 0000000..7fd5717 --- /dev/null +++ b/testing_project/demos/test_parametrize.py @@ -0,0 +1,28 @@ +import pytest + + +def test_for_loop_simple(): + cases = [1, 2, 3] + for a in cases: + assert a > 0 + + +@pytest.mark.parametrize('a', [1, 2, 3]) +def test_parametrize_simple(a): + # This test will be run 3 times, with a=1, a=2, and a=3 + assert a > 0 + + +def test_for_loop_multiple(): + cases = [(1, 'hi', 'hi'), (2, 'no', 'nono')] + for a, b, expected in cases: + result = b * a + assert result == expected + + +@pytest.mark.parametrize('a, b, expected', [(1, 'hi', 'hi'), (2, 'no', 'nono')]) +def test_parametrize_multiple(a, b, expected): + # This test will be run 2 times, with a=1, b='hi', expected='hi' + # and a=2, b='no', expected='nono' + result = b * a + assert result == expected diff --git a/testing_project/logistic.py b/testing_project/logistic.py new file mode 100644 index 0000000..e49d1c2 --- /dev/null +++ b/testing_project/logistic.py @@ -0,0 +1 @@ +# Your code goes here diff --git a/testing_project/logistic_fit.py b/testing_project/logistic_fit.py new file mode 100644 index 0000000..1d38ac7 --- /dev/null +++ b/testing_project/logistic_fit.py @@ -0,0 +1,32 @@ +import numpy as np + +from logistic import iterate_f + + +def fit_r(xs): + """ Takes a population trajectory and returns the value of r that generated it. + + By far not the most efficient method, but it always finds the optimal value of r with 1/1000 + precision. + + Parameters + ---------- + xs : list of float + A population trajectory. + + Returns + ------- + r: float + The value of r that generated the population trajectory. + """ + xs = np.asarray(xs) + x0 = xs[0] + it = len(xs) - 1 + + def error(r): + return np.linalg.norm(xs - iterate_f(it, x0, r)) + + errors = [] + for r in np.linspace(0, 4, 4001): + errors.append((r, error(r))) + return min(errors, key=lambda x: x[1])[0] diff --git a/testing_project/plot_logistic.py b/testing_project/plot_logistic.py new file mode 100644 index 0000000..6227b5f --- /dev/null +++ b/testing_project/plot_logistic.py @@ -0,0 +1,70 @@ +"""Usage: +``` +plot_trajectory(100, 3.6, 0.1) +plot_bifurcation(2.5, 4.2, 0.001) +``` +""" +import numpy as np +from matplotlib import pyplot as plt + +from logistic import iterate_f + + +def plot_trajectory(n, r, x0, fname="single_trajectory.png"): + """ + Saves a plot of a single trajectory of the logistic function + + inputs + n: int (number of iterations) + r: float (r value for the logistic function) + x0: float (between 0 and 1, starting point for the iteration) + fname: str (filename to which to save the image) + + returns + fig, ax (matplotlib objects) + """ + xs = iterate_f(n, x0, r) + fig, ax = plt.subplots(figsize=(10, 5)) + ax.plot(list(range(n)), xs) + fig.suptitle('Logistic Function') + + fig.savefig(fname) + return fig, ax + + +def plot_bifurcation(start, end, step, fname="bifurcation.png", it=100000, + last=300): + """ + Saves a plot of the bifurcation diagram of the logistic function. The + `start`, `end`, and `step` parameters define for which r values to + calculate the logistic function. If you space them too closely, it might + take a very long time, if you dont plot enough, your bifurcation diagram + won't be informative. Choose wisely! + + inputs + start, end, step: float (which r values to calculate the logistic + function for) + fname: str (filename to which to save the image) + it: int (how many iterations to run for each r value) + last: int (how many of the last iterates to plot) + + + returns + fig, ax (matplotlib objects) + """ + r_range = np.arange(start, end, step) + x = [] + y = [] + + for r in r_range: + xs = iterate_f(it, 0.1, r) + all_xs = xs[len(xs) - last::].copy() + unique_xs = np.unique(all_xs) + y.extend(unique_xs) + x.extend(np.ones(len(unique_xs)) * r) + + fig, ax = plt.subplots(figsize=(20, 10)) + ax.scatter(x, y, s=0.1, color='k') + ax.set_xlabel("r") + fig.savefig(fname) + return fig, ax diff --git a/testing_project/pytest.ini b/testing_project/pytest.ini new file mode 100644 index 0000000..6a71261 --- /dev/null +++ b/testing_project/pytest.ini @@ -0,0 +1,4 @@ +# pytest.ini +[pytest] +norecursedirs = * + diff --git a/testing_project/solution/conftest.py b/testing_project/solution/conftest.py new file mode 100644 index 0000000..4069350 --- /dev/null +++ b/testing_project/solution/conftest.py @@ -0,0 +1,28 @@ +import numpy as np +import pytest + + +# add a commandline option to pytest +def pytest_addoption(parser): + """Add random seed option to py.test. + """ + parser.addoption('--seed', dest='seed', type=int, action='store', + help='set random seed') + + +# configure pytest to automatically set the rnd seed if not passed on CLI +def pytest_configure(config): + seed = config.getvalue("seed") + # if seed was not set by the user, we set one now + if seed is None or seed == ('NO', 'DEFAULT'): + config.option.seed = int(np.random.randint(2 ** 31 - 1)) + + +def pytest_report_header(config): + return f'Using random seed: {config.option.seed}' + + +@pytest.fixture +def random_state(request): + random_state = np.random.RandomState(request.config.option.seed) + return random_state diff --git a/testing_project/solution/logistic.py b/testing_project/solution/logistic.py new file mode 100644 index 0000000..c2d8978 --- /dev/null +++ b/testing_project/solution/logistic.py @@ -0,0 +1,24 @@ +import numpy as np + + +def f(x, r): + """ Compute the logistic map for a given value of x and r. """ + return r * x * (1 - x) + + +def iterate_f(it, x0, r): + """ Generate a population trajectory. + + Takes a number of iterations `it`, a starting value, x0, + and a parameter value for r. It executes f repeatedly (it times), + each time using the last result of f as the new input to f. Append each + iteration's result to a list l. Finally, convert the list into a numpy + array and return it. + """ + x = x0 + xs = [x0] + for _ in range(it): + x = f(x, r) + xs.append(x) + + return np.array(xs) diff --git a/testing_project/solution/logistic_fit.py b/testing_project/solution/logistic_fit.py new file mode 100644 index 0000000..1d38ac7 --- /dev/null +++ b/testing_project/solution/logistic_fit.py @@ -0,0 +1,32 @@ +import numpy as np + +from logistic import iterate_f + + +def fit_r(xs): + """ Takes a population trajectory and returns the value of r that generated it. + + By far not the most efficient method, but it always finds the optimal value of r with 1/1000 + precision. + + Parameters + ---------- + xs : list of float + A population trajectory. + + Returns + ------- + r: float + The value of r that generated the population trajectory. + """ + xs = np.asarray(xs) + x0 = xs[0] + it = len(xs) - 1 + + def error(r): + return np.linalg.norm(xs - iterate_f(it, x0, r)) + + errors = [] + for r in np.linspace(0, 4, 4001): + errors.append((r, error(r))) + return min(errors, key=lambda x: x[1])[0] diff --git a/testing_project/solution/test_logistic.py b/testing_project/solution/test_logistic.py new file mode 100644 index 0000000..ce7f7de --- /dev/null +++ b/testing_project/solution/test_logistic.py @@ -0,0 +1,54 @@ +import numpy as np +from numpy.testing import assert_allclose +import pytest + +from logistic import f, iterate_f + + +def test_f(): + # Test cases are (x, r, expected) + cases = [ + (0.1, 2.2, 0.198), + (0.2, 3.4, 0.544), + (0.5, 2, 0.5), + ] + for x, r, expected in cases: + result = f(x, r) + assert_allclose(result, expected) + + +def test_f_corner_cases(): + # Test cases are (x, r, expected) + cases = [ + (0, 1.1, 0), + (1, 3.7, 0), + ] + for x, r, expected in cases: + result = f(x, r) + assert_allclose(result, expected) + + +def test_random_convergence(): + SEED = 42 + random_state = np.random.RandomState(SEED) + r = 1.5 + for _ in range(100): + x0 = random_state.uniform(0.0000001, 0.9999999) + xs = iterate_f(it=100, x0=x0, r=r) + assert np.isclose(xs[-1], 1 / 3) + +# SEED = 42 +# @pytest.fixture +# def random_state(): +# print(f"Using seed {SEED}") +# random_state = np.random.RandomState(SEED) +# return random_state + + +#@pytest.mark.xfail +def test_random_convergence_decorator(random_state): + r = 1.5 + for _ in range(100): + x0 = random_state.uniform(0.0000001, 0.9999999) + xs = iterate_f(it=100, x0=x0, r=r) + assert np.isclose(xs[-1], 1 / 3) \ No newline at end of file diff --git a/testing_project/solution/test_logistic_fit.py b/testing_project/solution/test_logistic_fit.py new file mode 100644 index 0000000..5b830ec --- /dev/null +++ b/testing_project/solution/test_logistic_fit.py @@ -0,0 +1,29 @@ +import numpy as np +from numpy.testing import assert_allclose + +from logistic import iterate_f +from logistic_fit import fit_r + + +SEED = 42 + + +def test_logistic_fit(): + r = 3.123 + x0 = 0.322 + xs = iterate_f(it=27, x0=x0, r=r) + + assert_allclose(r, fit_r(xs), atol=1e-3) + + +def test_logistic_fit_randomized(): + random_state = np.random.RandomState(SEED) + # We test for 100 random values of x0 and r, to make sure that the function works in general. + for _ in range(100): + x0 = random_state.uniform(0.0001, 0.9999) + # Round `r` to 1/1000 to make sure that it matches the precision of the fit_r function, + # so that r can be exactly recovered. + r = round(random_state.uniform(0.001, 3.999), 3) + xs = iterate_f(it=17, x0=x0, r=r) + + assert_allclose(r, fit_r(xs), atol=1e-3) diff --git a/testing_project/solution/test_logistic_parametrize.py b/testing_project/solution/test_logistic_parametrize.py new file mode 100644 index 0000000..b067dc9 --- /dev/null +++ b/testing_project/solution/test_logistic_parametrize.py @@ -0,0 +1,38 @@ +from numpy.testing import assert_allclose +import pytest + +from logistic import f, iterate_f + + +@pytest.mark.parametrize('x, r, expected', [ + (0.1, 2.2, 0.198), + (0.2, 3.4, 0.544), + (0.5, 2, 0.5), + ] +) +def test_f(x, r, expected): + result = f(x, r) + assert_allclose(result, expected) + + +@pytest.mark.parametrize('x, r, expected', [ + (0, 1.1, 0), + (1, 3.7, 0), + ] +) +def test_f_special_x_values(x, r, expected): + result = f(x, r) + assert_allclose(result, expected) + + +@pytest.mark.parametrize( + 'x, r, it, expected', + [ + (0.1, 2.2, 1, [0.1, 0.198]), + (0.2, 3.4, 4, [0.2, 0.544, 0.843418, 0.449019, 0.841163]), + (0.5, 2, 2, [0.5, 0.5, 0.5]), + ] +) +def test_iterate_f(x, r, it, expected): + result = iterate_f(it, x, r) + assert_allclose(result, expected, rtol=1e-5) diff --git a/testing_project/test_logistic.py b/testing_project/test_logistic.py new file mode 100644 index 0000000..9391bee --- /dev/null +++ b/testing_project/test_logistic.py @@ -0,0 +1,16 @@ +from numpy.testing import assert_allclose + +from logistic import f + +# Add here your test for the logistic map + + +def test_f_corner_cases(): + # Test cases are (x, r, expected) + cases = [ + (0, 1.1, 0), + (1, 3.7, 0), + ] + for x, r, expected in cases: + result = f(x, r) + assert_allclose(result, expected)