




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()












from itertools import count
from math import asin, pi, sqrt
def 							__lowerCAmelCase			(UpperCAmelCase_		):
    return (
        (1 - 2 * point) * sqrt(point - point**2		) + 2 * point + asin(sqrt(1 - point		)		)
    ) / 4
def 							__lowerCAmelCase			(UpperCAmelCase_		):
    a__  			=							(circles_number + 1 - sqrt(2 * circles_number		)) / (
        2 * (circles_number**2 + 1)
    )
    a__  			=							circles_number * intersection_y

    a__  			=							intersection_x * intersection_y / 2
    a__  			=							circle_bottom_arc_integral(
        1 / 2		) - circle_bottom_arc_integral(UpperCAmelCase_		)

    return triangle_area + concave_region_area
def 							__lowerCAmelCase			(UpperCAmelCase_ = 1 / 1_000		):
    a__  			=							(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() = }")






