






"""simple docstring"""





from itertools import product



def      __lowercase       (     a			:					int = 15			)       ->       int:
      __snake_case   :     List[Any]	      =0.0
      __snake_case   :     Dict	      =42
      __snake_case   :     Any	      =42
      __snake_case   :     Union[str, Any]	      =42
      __snake_case   :     Optional[Any]	      =42
      __snake_case   :     int	      =42
      __snake_case   :     int	      =42

      for series in product(range(2			)							,		repeat=a			):
            __snake_case   :     int	      =series.count(1			)
            __snake_case   :     Tuple	      =num_turns - num_blue
            if num_red >= num_blue:
                  continue
            __snake_case   :     Union[str, 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 typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_flax_available,
    is_sentencepiece_available,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


lowercase__				:				Dict						=      {
    "configuration_switch_transformers": [
        "SWITCH_TRANSFORMERS_PRETRAINED_CONFIG_ARCHIVE_MAP",
        "SwitchTransformersConfig",
        "SwitchTransformersOnnxConfig",
    ]
}

try:
				if not is_torch_available():
								raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
				pass
else:
				lowercase__				:				List[Any]						=      [
				    "SWITCH_TRANSFORMERS_PRETRAINED_MODEL_ARCHIVE_LIST",
				    "SwitchTransformersEncoderModel",
				    "SwitchTransformersForConditionalGeneration",
				    "SwitchTransformersModel",
				    "SwitchTransformersPreTrainedModel",
				    "SwitchTransformersTop1Router",
				    "SwitchTransformersSparseMLP",
				]


if TYPE_CHECKING:
				from .configuration_switch_transformers import (
				    SWITCH_TRANSFORMERS_PRETRAINED_CONFIG_ARCHIVE_MAP,
				    SwitchTransformersConfig,
				    SwitchTransformersOnnxConfig,
				)

				try:
								if not is_torch_available():
												raise OptionalDependencyNotAvailable()
				except OptionalDependencyNotAvailable:
								pass
				else:
								from .modeling_switch_transformers import (
								    SWITCH_TRANSFORMERS_PRETRAINED_MODEL_ARCHIVE_LIST,
								    SwitchTransformersEncoderModel,
								    SwitchTransformersForConditionalGeneration,
								    SwitchTransformersModel,
								    SwitchTransformersPreTrainedModel,
								    SwitchTransformersSparseMLP,
								    SwitchTransformersTopaRouter,
								)


else:
				import sys

				lowercase__				:				List[Any]						=      _LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)




