'''simple docstring'''





import math



class   UpperCamelCase					:







    """simple docstring"""





    def __init__(					self     :						List[Any]							,							UpperCAmelCase_     :						str							,							UpperCAmelCase_     :						Tuple							,							UpperCAmelCase_     :						Union[str, Any]):


         """simple docstring"""







         a					:							Any							= x
         a					:							Tuple							= y
         a					:							Tuple							= z







    def __repr__(					self     :						Union[str, Any]):


         """simple docstring"""







         return f"""Point({self.x}, {self.y}, {self.z})"""






def SCREAMING_SNAKE_CASE__  (				snake_case       :				Point				,	snake_case       :				Point  )   ->				float:







     """simple docstring"""
     return math.sqrt(abs((b.x - a.x) ** 2 + (b.y - a.y) ** 2 + (b.z - a.z) ** 2  )  )


if __name__ == "__main__":
      import doctest

      doctest.testmod()


'''simple docstring'''





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






def SCREAMING_SNAKE_CASE__  (				snake_case       :				float  )   ->				float:







     """simple docstring"""
     return (
         (1 - 2 * point) * sqrt(point - point**2  ) + 2 * point + asin(sqrt(1 - point  )  )
     ) / 4






def SCREAMING_SNAKE_CASE__  (				snake_case       :				int  )   ->				float:







     """simple docstring"""
     a					:							List[str]							= (circles_number + 1 - sqrt(2 * circles_number  )) / (
         2 * (circles_number**2 + 1)
     )
     a					:							int							= circles_number * intersection_y

     a					:							List[Any]							= intersection_x * intersection_y / 2
     a					:							List[str]							= circle_bottom_arc_integral(
         1 / 2  ) - circle_bottom_arc_integral(snake_case  )

     return triangle_area + concave_region_area






def SCREAMING_SNAKE_CASE__  (				snake_case       :				float = 1 / 1_000  )   ->				int:







     """simple docstring"""
     a					:							str							= (1 - pi / 4) / 4

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

     return -1


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

