



"""simple docstring"""

from itertools import product





def       __magic_name__    (   _lowerCamelCase				: int  ,       _lowerCamelCase				: int					):
							__a		:		Dict									=       sides_number
							__a		:		Optional[Any]									=       max_face_number * dice_number
							__a		:		str									=       [0] * (max_total + 1)

							__a		:		Optional[int]									=       1
							__a		:		List[Any]									=       range(_lowerCamelCase  ,       max_face_number + 1					)
							for dice_numbers in product(_lowerCamelCase  ,       repeat=_lowerCamelCase					):
														__a		:		List[Any]									=       sum(_lowerCamelCase					)
														totals_frequencies[total] += 1

							return totals_frequencies





def       __magic_name__    (   ):
							__a		:		Optional[Any]									=       total_frequency_distribution(
							    sides_number=4  ,       dice_number=9					)
							__a		:		Optional[int]									=       total_frequency_distribution(
							    sides_number=6  ,       dice_number=6					)

							__a		:		Optional[Any]									=       0
							__a		:		Any									=       9
							__a		:		Union[str, Any]									=       4 * 9
							__a		:		Optional[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]					)

							__a		:		Union[str, Any]									=       (4**9) * (6**6)
							__a		:		List[str]									=       peter_wins_count / total_games_number

							__a		:		Dict									=       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_sentencepiece_available,
    is_tokenizers_available,
    is_torch_available,
)


lowercase__			   =  {
    "configuration_llama": ["LLAMA_PRETRAINED_CONFIG_ARCHIVE_MAP", "LlamaConfig"],
}

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

try:
	if not is_tokenizers_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	lowercase__			   =  ["LlamaTokenizerFast"]

try:
	if not is_torch_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	lowercase__			   =  [
	    "LlamaForCausalLM",
	    "LlamaModel",
	    "LlamaPreTrainedModel",
	    "LlamaForSequenceClassification",
	]


if TYPE_CHECKING:
	from .configuration_llama import LLAMA_PRETRAINED_CONFIG_ARCHIVE_MAP, LlamaConfig

	try:
		if not is_sentencepiece_available():
			raise OptionalDependencyNotAvailable()
	except OptionalDependencyNotAvailable:
		pass
	else:
		from .tokenization_llama import LlamaTokenizer

	try:
		if not is_tokenizers_available():
			raise OptionalDependencyNotAvailable()
	except OptionalDependencyNotAvailable:
		pass
	else:
		from .tokenization_llama_fast import LlamaTokenizerFast

	try:
		if not is_torch_available():
			raise OptionalDependencyNotAvailable()
	except OptionalDependencyNotAvailable:
		pass
	else:
		from .modeling_llama import LlamaForCausalLM, LlamaForSequenceClassification, LlamaModel, LlamaPreTrainedModel


else:
	import sys

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

