
from itertools import count
from math import asin, pi, sqrt
def 					lowerCAmelCase__     (    SCREAMING_SNAKE_CASE_	)							->						str:
			return (
			    (1 - 2 * point) * sqrt(point - point**2	) + 2 * point + asin(sqrt(1 - point	)	)
			) / 4
def 					lowerCAmelCase__     (    SCREAMING_SNAKE_CASE_	)							->						Tuple:
			lowerCAmelCase__ : List[str]   =						(circles_number + 1 - sqrt(2 * circles_number	)) / (
			    2 * (circles_number**2 + 1)
			)
			lowerCAmelCase__ : Tuple   =						circles_number * intersection_y

			lowerCAmelCase__ : Union[str, Any]   =						intersection_x * intersection_y / 2
			lowerCAmelCase__ : Optional[Any]   =						circle_bottom_arc_integral(
			    1 / 2	) - circle_bottom_arc_integral(UpperCAmelCase_	)

			return triangle_area + concave_region_area
def 					lowerCAmelCase__     (    SCREAMING_SNAKE_CASE_ = 1 / 1_000	)							->						Optional[int]:
			lowerCAmelCase__ : List[str]   =						(1 - pi / 4) / 4

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

			return -1


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





from __future__ import annotations

import random







class 		__UpperCAmelCase:





     """simple docstring"""



     __UpperCAmelCase						:			Optional[int]							=     6

     def __init__(   self			:							int     )      ->      Optional[Any]:






         """simple docstring"""
         a__  			=							list(range(1    ,					Dice.NUM_SIDES + 1     )     )






     def 					__SCREAMING_SNAKE_CASE		(   self			:							Union[str, Any]     )      ->      List[str]:






         """simple docstring"""
         return random.choice(self.sides     )






def 							__lowerCAmelCase			(UpperCAmelCase_ ,     UpperCAmelCase_ = 2		):
    a__  			=							[Dice() for i in range(UpperCAmelCase_		)]
    a__  			=							[0] * (len(UpperCAmelCase_		) * Dice.NUM_SIDES + 1)
    for _ in range(UpperCAmelCase_		):
        count_of_sum[sum(dice.roll() for dice in dices		)] += 1
    a__  			=							[round((count * 100) / num_throws ,     2		) for count in count_of_sum]
    return probability[num_dice:]  # remove probability of sums that never appear


if __name__ == "__main__":
 import doctest

 doctest.testmod()






