
from __future__ import annotations

import random

class __snake_case	:
    _a	:		Optional[int]=       6
    def __init__(						self   ):



           '''simple docstring'''







           lowercase							:  Optional[int] 			=   list(range(1	,Dice.NUM_SIDES + 1   )   )
    def    _SCREAMING_SNAKE_CASE (						self   ):



           '''simple docstring'''







           return random.choice(self.sides   )







def 		_snake_case(						SCREAMING_SNAKE_CASE__      ,			SCREAMING_SNAKE_CASE__ = 2       )				->					list[float]:
       lowercase							:  str 			=   [Dice() for i in range(SCREAMING_SNAKE_CASE__       )]
       lowercase							:  Dict 			=   [0] * (len(SCREAMING_SNAKE_CASE__       ) * Dice.NUM_SIDES + 1)
       for _ in range(SCREAMING_SNAKE_CASE__       ):
              count_of_sum[sum(dice.roll() for dice in dices       )] += 1
       lowercase							:  Optional[int] 			=   [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 __future__ import annotations







def 		_snake_case(						SCREAMING_SNAKE_CASE__       )				->					bool:
       lowercase							:  int
       lowercase							:  list[str] 			=   list(SCREAMING_SNAKE_CASE__       )
       lowercase			,    lowercase							:  Union[str, Any] 			=   _vector[:-1], int(_vector[-1]       )
       lowercase							:  list[int] 			=   [int(SCREAMING_SNAKE_CASE__       ) for digit in __vector]

       vector.reverse()
       for i, digit in enumerate(SCREAMING_SNAKE_CASE__       ):
              if i & 1 == 0:
                     lowercase							:  int 			=   digit * 2
                     if doubled > 9:
                            doubled -= 9
                     check_digit += doubled
              else:
                     check_digit += digit

       return check_digit % 10 == 0


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  assert is_luhn("""79927398713""")
  assert not is_luhn("""79927398714""")
