






from itertools import product
def       a__						(  A = 15					):
   lowercase__						:	float         = 0.0
   lowercase__						:	float
   lowercase__						:	int
   lowercase__						:	int
   lowercase__						:	int
   lowercase__						:	int
   lowercase__						:	tuple[int, ...]

   for series in product(range(2					)		,				repeat=A					):
      lowercase__						:	Optional[Any]         = series.count(1					)
      lowercase__						:	str         = num_turns - num_blue
      if num_red >= num_blue:
         continue
      lowercase__						:	Optional[Any]         = 1.0
      for ind, col in enumerate(A		,				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() = }')










from dataclasses import dataclass
from typing import Callable, Optional

import datasets
@dataclass
class        __snake_case(					datasets.BuilderConfig      ):
 lowercase :       Optional[Callable]		      =		None
 lowercase :       Optional[dict]		      =		None
 lowercase :       Optional[datasets.Features]		      =		None



 def 						UpperCAmelCase    (	self   :   int	):

    """simple docstring"""






    assert self.generator is not None, "generator must be specified"

    if self.gen_kwargs is None:
       lowercase__						:	List[Any]         = {}
class        __snake_case(					datasets.GeneratorBasedBuilder      ):
 lowercase :       Dict		      =		GeneratorConfig



 def 						UpperCAmelCase    (	self   :   Any	):

    """simple docstring"""






    return datasets.DatasetInfo(features=self.config.features	)



 def 						UpperCAmelCase    (	self   :   List[str] ,		UpperCAmelCase__   :   Optional[int]	):

    """simple docstring"""






    return [datasets.SplitGenerator(name=datasets.Split.TRAIN ,		gen_kwargs=self.config.gen_kwargs	)]







 def 						UpperCAmelCase    (	self   :   Dict ,		**UpperCAmelCase__   :   List[str]	):

    """simple docstring"""






    for idx, ex in enumerate(self.config.generator(**UpperCAmelCase__	)	):
       yield idx, ex


