


'''simple docstring'''






from itertools import product






def 						_A					(lowerCAmelCase__	:int = 15		) ->	int:




     '''simple docstring'''



     _a         =				0.0
     _a         =				42
     _a         =				42
     _a         =				42
     _a         =				42
     _a         =				42
     _a         =				42

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


UpperCamelCase_						:					Dict      				=			{
    """configuration_layoutlm""": ["""LAYOUTLM_PRETRAINED_CONFIG_ARCHIVE_MAP""", """LayoutLMConfig""", """LayoutLMOnnxConfig"""],
    """tokenization_layoutlm""": ["""LayoutLMTokenizer"""],
}

try:
    if not is_tokenizers_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    UpperCamelCase_						:					List[Any]      				=			["""LayoutLMTokenizerFast"""]

try:
    if not is_torch_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    UpperCamelCase_						:					Optional[Any]      				=			[
        """LAYOUTLM_PRETRAINED_MODEL_ARCHIVE_LIST""",
        """LayoutLMForMaskedLM""",
        """LayoutLMForSequenceClassification""",
        """LayoutLMForTokenClassification""",
        """LayoutLMForQuestionAnswering""",
        """LayoutLMModel""",
        """LayoutLMPreTrainedModel""",
    ]

try:
    if not is_tf_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    UpperCamelCase_						:					Optional[int]      				=			[
        """TF_LAYOUTLM_PRETRAINED_MODEL_ARCHIVE_LIST""",
        """TFLayoutLMForMaskedLM""",
        """TFLayoutLMForSequenceClassification""",
        """TFLayoutLMForTokenClassification""",
        """TFLayoutLMForQuestionAnswering""",
        """TFLayoutLMMainLayer""",
        """TFLayoutLMModel""",
        """TFLayoutLMPreTrainedModel""",
    ]


if TYPE_CHECKING:
    from .configuration_layoutlm import LAYOUTLM_PRETRAINED_CONFIG_ARCHIVE_MAP, LayoutLMConfig, LayoutLMOnnxConfig
    from .tokenization_layoutlm import LayoutLMTokenizer

    try:
        if not is_tokenizers_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .tokenization_layoutlm_fast import LayoutLMTokenizerFast

    try:
        if not is_torch_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .modeling_layoutlm import (
            LAYOUTLM_PRETRAINED_MODEL_ARCHIVE_LIST,
            LayoutLMForMaskedLM,
            LayoutLMForQuestionAnswering,
            LayoutLMForSequenceClassification,
            LayoutLMForTokenClassification,
            LayoutLMModel,
            LayoutLMPreTrainedModel,
        )
    try:
        if not is_tf_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .modeling_tf_layoutlm import (
            TF_LAYOUTLM_PRETRAINED_MODEL_ARCHIVE_LIST,
            TFLayoutLMForMaskedLM,
            TFLayoutLMForQuestionAnswering,
            TFLayoutLMForSequenceClassification,
            TFLayoutLMForTokenClassification,
            TFLayoutLMMainLayer,
            TFLayoutLMModel,
            TFLayoutLMPreTrainedModel,
        )

else:
    import sys

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


