





'''simple docstring'''







from itertools import count
from math import asin, pi, sqrt





def    _lowerCAmelCase						(						lowercase	)					->					float:
			return (
			    (1 - 2 * point) * sqrt(point - point**2	) + 2 * point + asin(sqrt(1 - point	)	)
			) / 4





def    _lowerCAmelCase						(						lowercase	)					->					float:
			__lowerCAmelCase											=				(circles_number + 1 - sqrt(2 * circles_number	)) / (
			    2 * (circles_number**2 + 1)
			)
			__lowerCAmelCase											=				circles_number * intersection_y

			__lowerCAmelCase											=				intersection_x * intersection_y / 2
			__lowerCAmelCase											=				circle_bottom_arc_integral(
			    1 / 2	) - circle_bottom_arc_integral(lowercase	)

			return triangle_area + concave_region_area





def    _lowerCAmelCase						(						lowercase = 1 / 1000	)					->					int:
			__lowerCAmelCase											=				(1 - pi / 4) / 4

			for n in count(1	):
						if concave_triangle_area(lowercase	) / l_section_area < fraction:
									return n

			return -1


if __name__ == "__main__":
	print(f'{solution() = }')








'''simple docstring'''







import unittest
from pathlib import Path
from tempfile import TemporaryDirectory
from unittest.mock import Mock, patch

import diffusers.utils.hub_utils





class     _UpperCAmelCase							(						unittest.TestCase   ):
		@patch("""diffusers.utils.hub_utils.get_full_repo_name"""			)
		def   lowerCamelCase__			(  self,__SCREAMING_SNAKE_CASE			):



					'''simple docstring'''

					__lowerCAmelCase											=				"""full_repo_name"""
					with TemporaryDirectory() as tmpdir:
								# Dummy args values
								__lowerCAmelCase											=				Mock()
								__lowerCAmelCase											=				tmpdir
								__lowerCAmelCase											=				0
								__lowerCAmelCase											=				"""hub_token"""
								__lowerCAmelCase											=				"""dataset_name"""
								__lowerCAmelCase											=				0.01
								__lowerCAmelCase											=				10_00_00
								__lowerCAmelCase											=				1_00_00
								__lowerCAmelCase											=				0.01
								__lowerCAmelCase											=				0.02
								__lowerCAmelCase											=				0.03
								__lowerCAmelCase											=				0.0005
								__lowerCAmelCase											=				0.00_0001
								__lowerCAmelCase											=				1
								__lowerCAmelCase											=				10
								__lowerCAmelCase											=				0.001
								__lowerCAmelCase											=				0.1
								__lowerCAmelCase											=				0.2
								__lowerCAmelCase											=				True

								# Model card mush be rendered and saved
								diffusers.utils.hub_utils.create_model_card(__SCREAMING_SNAKE_CASE,model_name="""model_name"""			)
								self.assertTrue((Path(__SCREAMING_SNAKE_CASE			) / """README.md""").is_file()			)

