





'''simple docstring'''


from itertools import product
def 							UpperCAmelCase_  (						__lowerCamelCase : int     ,__lowerCamelCase : int			):
   lowercase_      :str         =			sides_number
   lowercase_      :Union[str, Any]         =			max_face_number * dice_number
   lowercase_      :Optional[int]         =			[0] * (max_total + 1)

   lowercase_      :Optional[int]         =			1
   lowercase_      :Optional[int]         =			range(__lowerCamelCase     ,max_face_number + 1			)
   for dice_numbers in product(__lowerCamelCase     ,repeat=__lowerCamelCase			):
      lowercase_      :List[str]         =			sum(__lowerCamelCase			)
      totals_frequencies[total] += 1

   return totals_frequencies
def 							UpperCAmelCase_  (						):
   lowercase_      :Union[str, Any]         =			total_frequency_distribution(
       sides_number=4     ,dice_number=9			)
   lowercase_      :str         =			total_frequency_distribution(
       sides_number=6     ,dice_number=6			)

   lowercase_      :List[str]         =			0
   lowercase_      :Tuple         =			9
   lowercase_      :Optional[int]         =			4 * 9
   lowercase_      :Any         =			6
   for peter_total in range(__lowerCamelCase     ,max_peter_total + 1			):
      peter_wins_count += peter_totals_frequencies[peter_total] * sum(
          colin_totals_frequencies[min_colin_total:peter_total]			)

   lowercase_      :Tuple         =			(4**9) * (6**6)
   lowercase_      :List[Any]         =			peter_wins_count / total_games_number

   lowercase_      :Optional[Any]         =			round(__lowerCamelCase     ,ndigits=7			)

   return rounded_peter_win_probability


if __name__ == "__main__":
 print(F'''{solution() = }''')









'''simple docstring'''


from typing import TYPE_CHECKING

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


lowerCAmelCase :					int 							={
    '''configuration_clip''': [
        '''CLIP_PRETRAINED_CONFIG_ARCHIVE_MAP''',
        '''CLIPConfig''',
        '''CLIPOnnxConfig''',
        '''CLIPTextConfig''',
        '''CLIPVisionConfig''',
    ],
    '''processing_clip''': ['''CLIPProcessor'''],
    '''tokenization_clip''': ['''CLIPTokenizer'''],
}

try:
 if not is_tokenizers_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 lowerCAmelCase :					Any 							=['''CLIPTokenizerFast''']

try:
 if not is_vision_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 lowerCAmelCase :					str 							=['''CLIPFeatureExtractor''']
 lowerCAmelCase :					Optional[int] 							=['''CLIPImageProcessor''']

try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 lowerCAmelCase :					Any 							=[
     '''CLIP_PRETRAINED_MODEL_ARCHIVE_LIST''',
     '''CLIPModel''',
     '''CLIPPreTrainedModel''',
     '''CLIPTextModel''',
     '''CLIPTextModelWithProjection''',
     '''CLIPVisionModel''',
     '''CLIPVisionModelWithProjection''',
 ]

try:
 if not is_tf_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 lowerCAmelCase :					Union[str, Any] 							=[
     '''TF_CLIP_PRETRAINED_MODEL_ARCHIVE_LIST''',
     '''TFCLIPModel''',
     '''TFCLIPPreTrainedModel''',
     '''TFCLIPTextModel''',
     '''TFCLIPVisionModel''',
 ]

try:
 if not is_flax_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 lowerCAmelCase :					List[Any] 							=[
     '''FlaxCLIPModel''',
     '''FlaxCLIPPreTrainedModel''',
     '''FlaxCLIPTextModel''',
     '''FlaxCLIPTextPreTrainedModel''',
     '''FlaxCLIPVisionModel''',
     '''FlaxCLIPVisionPreTrainedModel''',
 ]


if TYPE_CHECKING:
 from .configuration_clip import (
     CLIP_PRETRAINED_CONFIG_ARCHIVE_MAP,
     CLIPConfig,
     CLIPOnnxConfig,
     CLIPTextConfig,
     CLIPVisionConfig,
 )
 from .processing_clip import CLIPProcessor
 from .tokenization_clip import CLIPTokenizer

 try:
  if not is_tokenizers_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .tokenization_clip_fast import CLIPTokenizerFast

 try:
  if not is_vision_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .feature_extraction_clip import CLIPFeatureExtractor
  from .image_processing_clip import CLIPImageProcessor

 try:
  if not is_torch_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_clip import (
      CLIP_PRETRAINED_MODEL_ARCHIVE_LIST,
      CLIPModel,
      CLIPPreTrainedModel,
      CLIPTextModel,
      CLIPTextModelWithProjection,
      CLIPVisionModel,
      CLIPVisionModelWithProjection,
  )

 try:
  if not is_tf_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_tf_clip import (
      TF_CLIP_PRETRAINED_MODEL_ARCHIVE_LIST,
      TFCLIPModel,
      TFCLIPPreTrainedModel,
      TFCLIPTextModel,
      TFCLIPVisionModel,
  )

 try:
  if not is_flax_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_flax_clip import (
      FlaxCLIPModel,
      FlaxCLIPPreTrainedModel,
      FlaxCLIPTextModel,
      FlaxCLIPTextPreTrainedModel,
      FlaxCLIPVisionModel,
      FlaxCLIPVisionPreTrainedModel,
  )


else:
 import sys

 lowerCAmelCase :					int 							=_LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)


