

from itertools import product







def       snake_case__    (       lowerCAmelCase_ = 15      ):





     """simple docstring"""







     SCREAMING_SNAKE_CASE										=0.0
     SCREAMING_SNAKE_CASE										=42
     SCREAMING_SNAKE_CASE										=42
     SCREAMING_SNAKE_CASE										=42
     SCREAMING_SNAKE_CASE										=42
     SCREAMING_SNAKE_CASE										=42
     SCREAMING_SNAKE_CASE										=42

     for series in product(range(2      ),   repeat=lowerCAmelCase_      ):
          SCREAMING_SNAKE_CASE										=series.count(1      )
          SCREAMING_SNAKE_CASE										=num_turns - num_blue
          if num_red >= num_blue:
               continue
          SCREAMING_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() = }')




from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_sentencepiece_available, is_torch_available


_lowerCamelCase								={
    "configuration_xlm_prophetnet": ["XLM_PROPHETNET_PRETRAINED_CONFIG_ARCHIVE_MAP", "XLMProphetNetConfig"],
}

try:
 if not is_sentencepiece_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 _lowerCamelCase								=["XLMProphetNetTokenizer"]

try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 _lowerCamelCase								=[
     "XLM_PROPHETNET_PRETRAINED_MODEL_ARCHIVE_LIST",
     "XLMProphetNetDecoder",
     "XLMProphetNetEncoder",
     "XLMProphetNetForCausalLM",
     "XLMProphetNetForConditionalGeneration",
     "XLMProphetNetModel",
     "XLMProphetNetPreTrainedModel",
 ]


if TYPE_CHECKING:
 from .configuration_xlm_prophetnet import XLM_PROPHETNET_PRETRAINED_CONFIG_ARCHIVE_MAP, XLMProphetNetConfig

 try:
  if not is_sentencepiece_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .tokenization_xlm_prophetnet import XLMProphetNetTokenizer

 try:
  if not is_torch_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_xlm_prophetnet import (
      XLM_PROPHETNET_PRETRAINED_MODEL_ARCHIVE_LIST,
      XLMProphetNetDecoder,
      XLMProphetNetEncoder,
      XLMProphetNetForCausalLM,
      XLMProphetNetForConditionalGeneration,
      XLMProphetNetModel,
      XLMProphetNetPreTrainedModel,
  )

else:
 import sys

 _lowerCamelCase								=_LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)

