





'''simple docstring'''

from itertools import product




def  _a     (				lowerCAmelCase_ = 15						):





      """simple docstring"""



      _snake_case		:						float         =  0.0
      _snake_case		:						float
      _snake_case		:						int
      _snake_case		:						int
      _snake_case		:						int
      _snake_case		:						int
      _snake_case		:						tuple[int, ...]

      for series in product(range(2						)      ,   repeat=lowerCAmelCase_						):
            _snake_case		:						List[Any]         =  series.count(1						)
            _snake_case		:						Dict         =  num_turns - num_blue
            if num_red >= num_blue:
                  continue
            _snake_case		:						int         =  1.0
            for ind, col in enumerate(lowerCAmelCase_      ,   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() = }""")









'''simple docstring'''

from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_tf_available, is_torch_available


UpperCAmelCase       :		Dict		=				{'configuration_hubert': ['HUBERT_PRETRAINED_CONFIG_ARCHIVE_MAP', 'HubertConfig']}

try:
   if not is_torch_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   UpperCAmelCase       :		Union[str, Any]		=				[
       'HUBERT_PRETRAINED_MODEL_ARCHIVE_LIST',
       'HubertForCTC',
       'HubertForSequenceClassification',
       'HubertModel',
       'HubertPreTrainedModel',
   ]


try:
   if not is_tf_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   UpperCAmelCase       :		Optional[int]		=				[
       'TF_HUBERT_PRETRAINED_MODEL_ARCHIVE_LIST',
       'TFHubertForCTC',
       'TFHubertModel',
       'TFHubertPreTrainedModel',
   ]

if TYPE_CHECKING:
   from .configuration_hubert import HUBERT_PRETRAINED_CONFIG_ARCHIVE_MAP, HubertConfig

   try:
      if not is_torch_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_hubert import (
          HUBERT_PRETRAINED_MODEL_ARCHIVE_LIST,
          HubertForCTC,
          HubertForSequenceClassification,
          HubertModel,
          HubertPreTrainedModel,
      )

   try:
      if not is_tf_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_tf_hubert import (
          TF_HUBERT_PRETRAINED_MODEL_ARCHIVE_LIST,
          TFHubertForCTC,
          TFHubertModel,
          TFHubertPreTrainedModel,
      )


else:
   import sys

   UpperCAmelCase       :		Optional[int]		=				_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)


