






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


def 						_A     (       SCREAMING_SNAKE_CASE__						:			float ):
				return (
				    (1 - 2 * point) * sqrt(point - point**2 ) + 2 * point + asin(sqrt(1 - point ) )
				) / 4


def 						_A     (       SCREAMING_SNAKE_CASE__						:			int ):
				UpperCamelCase :str										=     (circles_number + 1 - sqrt(2 * circles_number )) / (
				    2 * (circles_number**2 + 1)
				)
				UpperCamelCase :List[Any]										=     circles_number * intersection_y

				UpperCamelCase :List[str]										=     intersection_x * intersection_y / 2
				UpperCamelCase :Optional[int]										=     circle_bottom_arc_integral(
				    1 / 2 ) - circle_bottom_arc_integral(SCREAMING_SNAKE_CASE__ )

				return triangle_area + concave_region_area


def 						_A     (       SCREAMING_SNAKE_CASE__						:			float = 1 / 1000 ):
				UpperCamelCase :Union[str, Any]										=     (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() = }''')













from __future__ import annotations







class     UpperCAmelCase_		:



      """simple docstring"""
      def __init__(       self					,       SCREAMING_SNAKE_CASE_				)       ->   None:
          UpperCamelCase :Tuple										=     value
          UpperCamelCase :Node | None										=     None
          UpperCamelCase :Node | None										=     None







class     UpperCAmelCase_		:



      """simple docstring"""
      UpperCamelCase_       :      int
      def __init__(       self				)       ->   None:
          UpperCamelCase :List[Any]										=     0
      def 					UpperCAmelCase		(       self					,       SCREAMING_SNAKE_CASE_					,       SCREAMING_SNAKE_CASE_				)       ->   None:
          if node is None:
              return

          if path_sum == self.target:
              self.paths += 1

          if node.left:
              self.depth_first_search(node.left					,       path_sum + node.left.value				)
          if node.right:
              self.depth_first_search(node.right					,       path_sum + node.right.value				)




      def 					UpperCAmelCase		(       self					,       SCREAMING_SNAKE_CASE_					,       SCREAMING_SNAKE_CASE_ = None				)       ->   int:
          if node is None:
              return 0
          if target is not None:
              UpperCamelCase :Tuple										=     target

          self.depth_first_search(SCREAMING_SNAKE_CASE_					,       node.value				)
          self.path_sum(node.left				)
          self.path_sum(node.right				)

          return self.paths


if __name__ == "__main__":
 import doctest

 doctest.testmod()





