



from itertools import product






def     a(      A       :    int ,     A       :    int       )		->       list[int]:
					"""simple docstring"""





					a					     =   sides_number
					a					     =   max_face_number * dice_number
					a					     =   [0] * (max_total + 1)

					a					     =   1
					a					     =   range(A ,     max_face_number + 1       )
					for dice_numbers in product(A ,     repeat=A       ):
										a					     =   sum(A       )
										totals_frequencies[total] += 1

					return totals_frequencies






def     a(      )		->       float:
					"""simple docstring"""





					a					     =   total_frequency_distribution(
					    sides_number=4 ,     dice_number=9       )
					a					     =   total_frequency_distribution(
					    sides_number=6 ,     dice_number=6       )

					a					     =   0
					a					     =   9
					a					     =   4 * 9
					a					     =   6
					for peter_total in range(A ,     max_peter_total + 1       ):
										peter_wins_count += peter_totals_frequencies[peter_total] * sum(
										    colin_totals_frequencies[min_colin_total:peter_total]       )

					a					     =   (4**9) * (6**6)
					a					     =   peter_wins_count / total_games_number

					a					     =   round(A ,     ndigits=7       )

					return rounded_peter_win_probability


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





from typing import TYPE_CHECKING

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


_lowercase: Union[str, Any]      			=		{
    "configuration_bridgetower": [
        "BRIDGETOWER_PRETRAINED_CONFIG_ARCHIVE_MAP",
        "BridgeTowerConfig",
        "BridgeTowerTextConfig",
        "BridgeTowerVisionConfig",
    ],
    "processing_bridgetower": ["BridgeTowerProcessor"],
}

try:
				if not is_vision_available():
								raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
				pass
else:
				_lowercase: Dict      			=		["BridgeTowerImageProcessor"]

try:
				if not is_torch_available():
								raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
				pass
else:
				_lowercase: int      			=		[
				    "BRIDGETOWER_PRETRAINED_MODEL_ARCHIVE_LIST",
				    "BridgeTowerForContrastiveLearning",
				    "BridgeTowerForImageAndTextRetrieval",
				    "BridgeTowerForMaskedLM",
				    "BridgeTowerModel",
				    "BridgeTowerPreTrainedModel",
				]


if TYPE_CHECKING:
				from .configuration_bridgetower import (
				    BRIDGETOWER_PRETRAINED_CONFIG_ARCHIVE_MAP,
				    BridgeTowerConfig,
				    BridgeTowerTextConfig,
				    BridgeTowerVisionConfig,
				)
				from .processing_bridgetower import BridgeTowerProcessor

				try:
								if not is_vision_available():
												raise OptionalDependencyNotAvailable()
				except OptionalDependencyNotAvailable:
								pass
				else:
								from .image_processing_bridgetower import BridgeTowerImageProcessor

				try:
								if not is_torch_available():
												raise OptionalDependencyNotAvailable()
				except OptionalDependencyNotAvailable:
								pass
				else:
								from .modeling_bridgetower import (
								    BRIDGETOWER_PRETRAINED_MODEL_ARCHIVE_LIST,
								    BridgeTowerForContrastiveLearning,
								    BridgeTowerForImageAndTextRetrieval,
								    BridgeTowerForMaskedLM,
								    BridgeTowerModel,
								    BridgeTowerPreTrainedModel,
								)


else:
				import sys

				_lowercase: Optional[Any]      			=		_LazyModule(__name__, globals()["__file__"], _import_structure)
