
'''simple docstring'''



from typing import TYPE_CHECKING

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


_lowercase          =						{
    """configuration_gpt_neo""": ["""GPT_NEO_PRETRAINED_CONFIG_ARCHIVE_MAP""", """GPTNeoConfig""", """GPTNeoOnnxConfig"""],
}

try:
						if not is_torch_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						_lowercase          =						[
						    """GPT_NEO_PRETRAINED_MODEL_ARCHIVE_LIST""",
						    """GPTNeoForCausalLM""",
						    """GPTNeoForQuestionAnswering""",
						    """GPTNeoForSequenceClassification""",
						    """GPTNeoForTokenClassification""",
						    """GPTNeoModel""",
						    """GPTNeoPreTrainedModel""",
						    """load_tf_weights_in_gpt_neo""",
						]

try:
						if not is_flax_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						_lowercase          =						[
						    """FlaxGPTNeoForCausalLM""",
						    """FlaxGPTNeoModel""",
						    """FlaxGPTNeoPreTrainedModel""",
						]


if TYPE_CHECKING:
						from .configuration_gpt_neo import GPT_NEO_PRETRAINED_CONFIG_ARCHIVE_MAP, GPTNeoConfig, GPTNeoOnnxConfig

						try:
												if not is_torch_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_gpt_neo import (
												    GPT_NEO_PRETRAINED_MODEL_ARCHIVE_LIST,
												    GPTNeoForCausalLM,
												    GPTNeoForQuestionAnswering,
												    GPTNeoForSequenceClassification,
												    GPTNeoForTokenClassification,
												    GPTNeoModel,
												    GPTNeoPreTrainedModel,
												    load_tf_weights_in_gpt_neo,
												)

						try:
												if not is_flax_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_flax_gpt_neo import FlaxGPTNeoForCausalLM, FlaxGPTNeoModel, FlaxGPTNeoPreTrainedModel


else:
						import sys

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


'''simple docstring'''



from itertools import product


def A (__lowerCamelCase :int					,      __lowerCamelCase :int						):
						_lowerCAmelCase    		=					sides_number
						_lowerCAmelCase    		=					max_face_number * dice_number
						_lowerCAmelCase    		=					[0] * (max_total + 1)

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

						return totals_frequencies


def A ():
						_lowerCAmelCase    		=					total_frequency_distribution(
						    sides_number=4					,      dice_number=9						)
						_lowerCAmelCase    		=					total_frequency_distribution(
						    sides_number=6					,      dice_number=6						)

						_lowerCAmelCase    		=					0
						_lowerCAmelCase    		=					9
						_lowerCAmelCase    		=					4 * 9
						_lowerCAmelCase    		=					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]						)

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

						_lowerCAmelCase    		=					round(__lowerCamelCase					,      ndigits=7						)

						return rounded_peter_win_probability


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