


"""simple docstring"""






from itertools import product
def      lowerCamelCase       (     _UpperCamelCase		:      int       ,			_UpperCamelCase		:      int							)		->       list[int]:

							'''simple docstring'''



							__UpperCAmelCase   :						Union[str, Any]      							=					sides_number
							__UpperCAmelCase   :						Tuple      							=					max_face_number * dice_number
							__UpperCAmelCase   :						Optional[Any]      							=					[0] * (max_total + 1)

							__UpperCAmelCase   :						Tuple      							=					1
							__UpperCAmelCase   :						List[Any]      							=					range(_UpperCamelCase       ,			max_face_number + 1							)
							for dice_numbers in product(_UpperCamelCase       ,			repeat=_UpperCamelCase							):
														__UpperCAmelCase   :						int      							=					sum(_UpperCamelCase							)
														totals_frequencies[total] += 1

							return totals_frequencies
def      lowerCamelCase       (     )		->       float:

							'''simple docstring'''



							__UpperCAmelCase   :						Optional[int]      							=					total_frequency_distribution(
							    sides_number=4       ,			dice_number=9							)
							__UpperCAmelCase   :						Optional[int]      							=					total_frequency_distribution(
							    sides_number=6       ,			dice_number=6							)

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

							__UpperCAmelCase   :						List[Any]      							=					(4**9) * (6**6)
							__UpperCAmelCase   :						int      							=					peter_wins_count / total_games_number

							__UpperCAmelCase   :						Any      							=					round(_UpperCamelCase       ,			ndigits=7							)

							return rounded_peter_win_probability


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




"""simple docstring"""






from ...utils import (
    OptionalDependencyNotAvailable,
    is_torch_available,
    is_transformers_available,
    is_transformers_version,
)


try:
							if not (is_transformers_available() and is_torch_available()):
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							from ...utils.dummy_torch_and_transformers_objects import (
							    ImageTextPipelineOutput,
							    UniDiffuserPipeline,
							)
else:
							from .modeling_text_decoder import UniDiffuserTextDecoder
							from .modeling_uvit import UniDiffuserModel, UTransformeraDModel
							from .pipeline_unidiffuser import ImageTextPipelineOutput, UniDiffuserPipeline
