






"""simple docstring"""


from typing import TYPE_CHECKING

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


lowercase_    					=					{
    'configuration_bart': ['BART_PRETRAINED_CONFIG_ARCHIVE_MAP', 'BartConfig', 'BartOnnxConfig'],
    'tokenization_bart': ['BartTokenizer'],
}

try:
       if not is_tokenizers_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       lowercase_    					=					['BartTokenizerFast']

try:
       if not is_torch_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       lowercase_    					=					[
           'BART_PRETRAINED_MODEL_ARCHIVE_LIST',
           'BartForCausalLM',
           'BartForConditionalGeneration',
           'BartForQuestionAnswering',
           'BartForSequenceClassification',
           'BartModel',
           'BartPretrainedModel',
           'PretrainedBartModel',
       ]

try:
       if not is_tf_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       lowercase_    					=					[
           'TFBartForConditionalGeneration',
           'TFBartForSequenceClassification',
           'TFBartModel',
           'TFBartPretrainedModel',
       ]

try:
       if not is_flax_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       lowercase_    					=					[
           'FlaxBartDecoderPreTrainedModel',
           'FlaxBartForCausalLM',
           'FlaxBartForConditionalGeneration',
           'FlaxBartForQuestionAnswering',
           'FlaxBartForSequenceClassification',
           'FlaxBartModel',
           'FlaxBartPreTrainedModel',
       ]

if TYPE_CHECKING:
       from .configuration_bart import BART_PRETRAINED_CONFIG_ARCHIVE_MAP, BartConfig, BartOnnxConfig
       from .tokenization_bart import BartTokenizer

       try:
              if not is_tokenizers_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .tokenization_bart_fast import BartTokenizerFast

       try:
              if not is_torch_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .modeling_bart import (
                  BART_PRETRAINED_MODEL_ARCHIVE_LIST,
                  BartForCausalLM,
                  BartForConditionalGeneration,
                  BartForQuestionAnswering,
                  BartForSequenceClassification,
                  BartModel,
                  BartPretrainedModel,
                  PretrainedBartModel,
              )

       try:
              if not is_tf_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .modeling_tf_bart import (
                  TFBartForConditionalGeneration,
                  TFBartForSequenceClassification,
                  TFBartModel,
                  TFBartPretrainedModel,
              )

       try:
              if not is_flax_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .modeling_flax_bart import (
                  FlaxBartDecoderPreTrainedModel,
                  FlaxBartForCausalLM,
                  FlaxBartForConditionalGeneration,
                  FlaxBartForQuestionAnswering,
                  FlaxBartForSequenceClassification,
                  FlaxBartModel,
                  FlaxBartPreTrainedModel,
              )

else:
       import sys

       lowercase_    					=					_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)












"""simple docstring"""


from itertools import product



def  lowerCAmelCase    (   __UpperCamelCase = 1_5			):




  """simple docstring"""







  __A						      =			0.0
  __A						      =			42
  __A						      =			42
  __A						      =			42
  __A						      =			42
  __A						      =			42
  __A						      =			42

  for series in product(range(2			)		,	repeat=__UpperCamelCase			):
    __A						      =			series.count(1			)
    __A						      =			num_turns - num_blue
    if num_red >= num_blue:
      continue
    __A						      =			1.0
    for ind, col in enumerate(__UpperCamelCase		,	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() = }''')




