






"""simple docstring"""


from ..utils import DummyObject, requires_backends


class  snake_case		(							metaclass=_lowerCAmelCase						):


   '''simple docstring'''

   A_						:     str									=			["torch", "transformers", "invisible_watermark"]


   def __init__(     self			:					str,	*_lowerCamelCase			:					int,	**_lowerCamelCase			:					Dict  ):

     '''simple docstring'''
     requires_backends(self,	['''torch''', '''transformers''', '''invisible_watermark''']  )


   @classmethod
   def     _SCREAMING_SNAKE_CASE    (     cls			:					Tuple,	*_lowerCamelCase			:					Any,	**_lowerCamelCase			:					Union[str, Any]  ):

     '''simple docstring'''
     requires_backends(cls,	['''torch''', '''transformers''', '''invisible_watermark''']  )






   @classmethod
   def     _SCREAMING_SNAKE_CASE    (     cls			:					Union[str, Any],	*_lowerCamelCase			:					str,	**_lowerCamelCase			:					Optional[Any]  ):

     '''simple docstring'''
     requires_backends(cls,	['''torch''', '''transformers''', '''invisible_watermark''']  )





class  snake_case		(							metaclass=_lowerCAmelCase						):


   '''simple docstring'''

   A_						:     Any									=			["torch", "transformers", "invisible_watermark"]


   def __init__(     self			:					Dict,	*_lowerCamelCase			:					Optional[int],	**_lowerCamelCase			:					int  ):

     '''simple docstring'''
     requires_backends(self,	['''torch''', '''transformers''', '''invisible_watermark''']  )


   @classmethod
   def     _SCREAMING_SNAKE_CASE    (     cls			:					str,	*_lowerCamelCase			:					Any,	**_lowerCamelCase			:					Any  ):

     '''simple docstring'''
     requires_backends(cls,	['''torch''', '''transformers''', '''invisible_watermark''']  )






   @classmethod
   def     _SCREAMING_SNAKE_CASE    (     cls			:					Any,	*_lowerCamelCase			:					int,	**_lowerCamelCase			:					Tuple  ):

     '''simple docstring'''
     requires_backends(cls,	['''torch''', '''transformers''', '''invisible_watermark''']  )












"""simple docstring"""


from itertools import product



def  lowerCAmelCase    (   __UpperCamelCase = 1_5			):




  """simple docstring"""







  __A						      =			0.0
  __A						      =			42
  __A						      =			42
  __A						      =			42
  __A						      =			42
  __A						      =			42
  __A						      =			42

  for series in product(range(2			)		,	repeat=__UpperCamelCase			):
    __A						      =			series.count(1			)
    __A						      =			num_turns - num_blue
    if num_red >= num_blue:
      continue
    __A						      =			1.0
    for ind, col in enumerate(__UpperCamelCase		,	2			):
      if col == 0:
        prob *= (ind - 1) / ind
      else:
        prob *= 1 / ind

    total_prob += prob

  return int(1 / total_prob			)


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




