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




def 					lowerCamelCase__					(    a__	:	Any  )		->						Dict:
       return (
           (1 - 2 * point) * sqrt(point - point**2  ) + 2 * point + asin(sqrt(1 - point  )  )
       ) / 4




def 					lowerCamelCase__					(    a__	:	Any  )		->						Optional[int]:
       UpperCamelCase_											=							(circles_number + 1 - sqrt(2 * circles_number  )) / (
           2 * (circles_number**2 + 1)
       )
       UpperCamelCase_											=							circles_number * intersection_y

       UpperCamelCase_											=							intersection_x * intersection_y / 2
       UpperCamelCase_											=							circle_bottom_arc_integral(
           1 / 2  ) - circle_bottom_arc_integral(SCREAMING_SNAKE_CASE__  )

       return triangle_area + concave_region_area




def 					lowerCamelCase__					(    a__	:	Union[str, Any] = 1 / 1000  )		->						Tuple:
       UpperCamelCase_											=							(1 - pi / 4) / 4

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

       return -1


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








def  _UpperCAmelCase  (				SCREAMING_SNAKE_CASE__  ):


						'''simple docstring'''




						lowerCAmelCase	:   List[str]					     =					str(SCREAMING_SNAKE_CASE__  ).strip()
						if not bin_string:
												raise ValueError("""Empty string was passed to the function"""  )
						lowerCAmelCase	:   Optional[int]					     =					bin_string[0] == """-"""
						if is_negative:
												lowerCAmelCase	:   Tuple					     =					bin_string[1:]
						if not all(char in """01""" for char in bin_string  ):
												raise ValueError("""Non-binary value was passed to the function"""  )
						lowerCAmelCase	:   Union[str, Any]					     =					0
						for char in bin_string:
												lowerCAmelCase	:   int					     =					2 * decimal_number + int(SCREAMING_SNAKE_CASE__  )
						return -decimal_number if is_negative else decimal_number


if __name__ == "__main__":
		from doctest import testmod

		testmod()

