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

def   a_					(_lowerCAmelCase  :   Union[str, Any]       )->				float:
    return (
        (1 - 2 * point) * sqrt(point - point**2       ) + 2 * point + asin(sqrt(1 - point       )       )
    ) / 4

def   a_					(_lowerCAmelCase  :   Union[str, Any]       )->				float:
    snake_case:						Optional[Any]         =   (circles_number + 1 - sqrt(2 * circles_number       )) / (
        2 * (circles_number**2 + 1)
    )
    snake_case:						Optional[int]         =   circles_number * intersection_y

    snake_case:						Union[str, Any]         =   intersection_x * intersection_y / 2
    snake_case:						Any         =   circle_bottom_arc_integral(
        1 / 2       ) - circle_bottom_arc_integral(_lowerCAmelCase       )

    return triangle_area + concave_region_area

def   a_					(_lowerCAmelCase  :   Optional[int] = 1 / 1000       )->				int:
    snake_case:						str         =   (1 - pi / 4) / 4

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

    return -1


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






class     __a     :
 def __init__(  self					)   ->							Tuple:




        '''simple docstring'''
        lowercase__:  str         =  []
        lowercase__:  Any         =  0
        lowercase__:  int         =  0
 def __str__(  self					)   ->							Any:




        '''simple docstring'''
        lowercase__:  str         =  '<' + str(self.entries					)[1:-1] + '>'
        return printed
 def 						SCREAMING_SNAKE_CASE__  (  self							,					lowerCAmelCase__					)   ->							List[str]:




        '''simple docstring'''
        self.entries.append(lowerCAmelCase__					)
        lowercase__:  List[str]         =  self.length + 1
 def 						SCREAMING_SNAKE_CASE__  (  self					)   ->							str:




        '''simple docstring'''
        lowercase__:  Any         =  self.length - 1
        lowercase__:  Optional[int]         =  self.entries[self.front]
        # self.front-=1
        # self.entries = self.entries[self.front:]
        lowercase__:  int         =  self.entries[1:]
        return dequeued
 def 						SCREAMING_SNAKE_CASE__  (  self							,					lowerCAmelCase__					)   ->							List[str]:




        '''simple docstring'''
        for _ in range(lowerCAmelCase__					):
               self.put(self.get()					)
 def 						SCREAMING_SNAKE_CASE__  (  self					)   ->							Union[str, Any]:




        '''simple docstring'''
        return self.entries[0]
 def 						SCREAMING_SNAKE_CASE__  (  self					)   ->							Optional[int]:




        '''simple docstring'''
        return self.length


