

from __future__ import annotations

import random





class       __UpperCAmelCase  :
   UpperCamelCase       =  6



   def __init__(							self							:  Union[str, Any]		):
     UpperCAmelCase :							List[Any]								=				list(range(1,	Dice.NUM_SIDES + 1		)		)





   def  __magic_name__					(							self							:  int		):
     return random.choice(self.sides		)






def     a__  (	UpperCAmelCase							:    int       ,				UpperCAmelCase							:    int = 2    )						->		list[float]:
  UpperCAmelCase :							Union[str, Any]								=				[Dice() for i in range(UpperCAmelCase    )]
  UpperCAmelCase :							Optional[Any]								=				[0] * (len(UpperCAmelCase    ) * Dice.NUM_SIDES + 1)
  for _ in range(UpperCAmelCase    ):
    count_of_sum[sum(dice.roll() for dice in dices    )] += 1
  UpperCAmelCase :							List[Any]								=				[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()








import decimal

def     a__  (	)						->		int:
  UpperCAmelCase :							List[Any]								=				0
  UpperCAmelCase :							Dict								=				decimal.Context(prec=105    )
  for i in range(2       ,				100    ):
    UpperCAmelCase :							List[str]								=				decimal.Decimal(UpperCAmelCase    )
    UpperCAmelCase :							List[str]								=				number.sqrt(UpperCAmelCase    )
    if len(str(UpperCAmelCase    )    ) > 1:
      answer += int(str(UpperCAmelCase    )[0]    )
      UpperCAmelCase :							str								=				str(UpperCAmelCase    )[2:101]
      answer += sum(int(UpperCAmelCase    ) for x in sqrt_number_str    )
  return answer


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     print(f"""{solution() = }""")





