




'''simple docstring'''



from itertools import product







def 	_UpperCamelCase       (_lowerCamelCase							:   int = 15		)->      int:




     '''simple docstring'''





     __snake_case			    =     0.0
     __snake_case			    =     42
     __snake_case			    =     42
     __snake_case			    =     42
     __snake_case			    =     42
     __snake_case			    =     42
     __snake_case			    =     42

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


UpperCAmelCase_				:     Dict     			=						{
    '''configuration_markuplm''': ['''MARKUPLM_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''MarkupLMConfig'''],
    '''feature_extraction_markuplm''': ['''MarkupLMFeatureExtractor'''],
    '''processing_markuplm''': ['''MarkupLMProcessor'''],
    '''tokenization_markuplm''': ['''MarkupLMTokenizer'''],
}

try:
     if not is_tokenizers_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     UpperCAmelCase_				:     List[Any]     			=						['''MarkupLMTokenizerFast''']

try:
     if not is_torch_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     UpperCAmelCase_				:     int     			=						[
         '''MARKUPLM_PRETRAINED_MODEL_ARCHIVE_LIST''',
         '''MarkupLMForQuestionAnswering''',
         '''MarkupLMForSequenceClassification''',
         '''MarkupLMForTokenClassification''',
         '''MarkupLMModel''',
         '''MarkupLMPreTrainedModel''',
     ]


if TYPE_CHECKING:
     from .configuration_markuplm import MARKUPLM_PRETRAINED_CONFIG_ARCHIVE_MAP, MarkupLMConfig
     from .feature_extraction_markuplm import MarkupLMFeatureExtractor
     from .processing_markuplm import MarkupLMProcessor
     from .tokenization_markuplm import MarkupLMTokenizer

     try:
          if not is_tokenizers_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .tokenization_markuplm_fast import MarkupLMTokenizerFast

     try:
          if not is_torch_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .modeling_markuplm import (
              MARKUPLM_PRETRAINED_MODEL_ARCHIVE_LIST,
              MarkupLMForQuestionAnswering,
              MarkupLMForSequenceClassification,
              MarkupLMForTokenClassification,
              MarkupLMModel,
              MarkupLMPreTrainedModel,
          )


else:
     import sys

     UpperCAmelCase_				:     Dict     			=						_LazyModule(__name__, globals()['''__file__'''], _import_structure)






