

from itertools import product



def  __lowerCAmelCase (  A = 15      ):
	UpperCAmelCase_    			=     0.0
	UpperCAmelCase_    			=     42
	UpperCAmelCase_    			=     42
	UpperCAmelCase_    			=     42
	UpperCAmelCase_    			=     42
	UpperCAmelCase_    			=     42
	UpperCAmelCase_    			=     42

	for series in product(range(2      )    ,       repeat=A      ):
		UpperCAmelCase_    			=     series.count(1      )
		UpperCAmelCase_    			=     num_turns - num_blue
		if num_red >= num_blue:
			continue
		UpperCAmelCase_    			=     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_tokenizers_available, is_torch_available


_a:      Dict								=     {
    """configuration_nystromformer""": ["""NYSTROMFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP""", """NystromformerConfig"""],
}

try:
				if not is_torch_available():
								raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
				pass
else:
				_a:      Any								=     [
				    """NYSTROMFORMER_PRETRAINED_MODEL_ARCHIVE_LIST""",
				    """NystromformerForMaskedLM""",
				    """NystromformerForMultipleChoice""",
				    """NystromformerForQuestionAnswering""",
				    """NystromformerForSequenceClassification""",
				    """NystromformerForTokenClassification""",
				    """NystromformerLayer""",
				    """NystromformerModel""",
				    """NystromformerPreTrainedModel""",
				]


if TYPE_CHECKING:
				from .configuration_nystromformer import NYSTROMFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP, NystromformerConfig

				try:
								if not is_torch_available():
												raise OptionalDependencyNotAvailable()
				except OptionalDependencyNotAvailable:
								pass
				else:
								from .modeling_nystromformer import (
								    NYSTROMFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
								    NystromformerForMaskedLM,
								    NystromformerForMultipleChoice,
								    NystromformerForQuestionAnswering,
								    NystromformerForSequenceClassification,
								    NystromformerForTokenClassification,
								    NystromformerLayer,
								    NystromformerModel,
								    NystromformerPreTrainedModel,
								)


else:
				import sys

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