



'''simple docstring'''

from typing import TYPE_CHECKING

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


__lowerCAmelCase									=   {
    '''configuration_distilbert''': [
        '''DISTILBERT_PRETRAINED_CONFIG_ARCHIVE_MAP''',
        '''DistilBertConfig''',
        '''DistilBertOnnxConfig''',
    ],
    '''tokenization_distilbert''': ['''DistilBertTokenizer'''],
}

try:
							if not is_tokenizers_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							__lowerCAmelCase									=   ['''DistilBertTokenizerFast''']

try:
							if not is_torch_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							__lowerCAmelCase									=   [
							    '''DISTILBERT_PRETRAINED_MODEL_ARCHIVE_LIST''',
							    '''DistilBertForMaskedLM''',
							    '''DistilBertForMultipleChoice''',
							    '''DistilBertForQuestionAnswering''',
							    '''DistilBertForSequenceClassification''',
							    '''DistilBertForTokenClassification''',
							    '''DistilBertModel''',
							    '''DistilBertPreTrainedModel''',
							]

try:
							if not is_tf_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							__lowerCAmelCase									=   [
							    '''TF_DISTILBERT_PRETRAINED_MODEL_ARCHIVE_LIST''',
							    '''TFDistilBertForMaskedLM''',
							    '''TFDistilBertForMultipleChoice''',
							    '''TFDistilBertForQuestionAnswering''',
							    '''TFDistilBertForSequenceClassification''',
							    '''TFDistilBertForTokenClassification''',
							    '''TFDistilBertMainLayer''',
							    '''TFDistilBertModel''',
							    '''TFDistilBertPreTrainedModel''',
							]

try:
							if not is_flax_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							__lowerCAmelCase									=   [
							    '''FlaxDistilBertForMaskedLM''',
							    '''FlaxDistilBertForMultipleChoice''',
							    '''FlaxDistilBertForQuestionAnswering''',
							    '''FlaxDistilBertForSequenceClassification''',
							    '''FlaxDistilBertForTokenClassification''',
							    '''FlaxDistilBertModel''',
							    '''FlaxDistilBertPreTrainedModel''',
							]


if TYPE_CHECKING:
							from .configuration_distilbert import (
							    DISTILBERT_PRETRAINED_CONFIG_ARCHIVE_MAP,
							    DistilBertConfig,
							    DistilBertOnnxConfig,
							)
							from .tokenization_distilbert import DistilBertTokenizer

							try:
														if not is_tokenizers_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .tokenization_distilbert_fast import DistilBertTokenizerFast

							try:
														if not is_torch_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .modeling_distilbert import (
														    DISTILBERT_PRETRAINED_MODEL_ARCHIVE_LIST,
														    DistilBertForMaskedLM,
														    DistilBertForMultipleChoice,
														    DistilBertForQuestionAnswering,
														    DistilBertForSequenceClassification,
														    DistilBertForTokenClassification,
														    DistilBertModel,
														    DistilBertPreTrainedModel,
														)

							try:
														if not is_tf_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .modeling_tf_distilbert import (
														    TF_DISTILBERT_PRETRAINED_MODEL_ARCHIVE_LIST,
														    TFDistilBertForMaskedLM,
														    TFDistilBertForMultipleChoice,
														    TFDistilBertForQuestionAnswering,
														    TFDistilBertForSequenceClassification,
														    TFDistilBertForTokenClassification,
														    TFDistilBertMainLayer,
														    TFDistilBertModel,
														    TFDistilBertPreTrainedModel,
														)

							try:
														if not is_flax_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .modeling_flax_distilbert import (
														    FlaxDistilBertForMaskedLM,
														    FlaxDistilBertForMultipleChoice,
														    FlaxDistilBertForQuestionAnswering,
														    FlaxDistilBertForSequenceClassification,
														    FlaxDistilBertForTokenClassification,
														    FlaxDistilBertModel,
														    FlaxDistilBertPreTrainedModel,
														)

else:
							import sys

							__lowerCAmelCase									=   _LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)





'''simple docstring'''




from itertools import product




def 							lowerCamelCase	(      UpperCAmelCase__       :					int      ,      UpperCAmelCase__       :					int )			->      list[int]:
							lowercase_					:			List[Any]										=       sides_number
							lowercase_					:			Dict										=       max_face_number * dice_number
							lowercase_					:			List[str]										=       [0] * (max_total + 1)

							lowercase_					:			Union[str, Any]										=       1
							lowercase_					:			Dict										=       range(UpperCAmelCase__      ,      max_face_number + 1 )
							for dice_numbers in product(UpperCAmelCase__      ,      repeat=UpperCAmelCase__ ):
														lowercase_					:			Any										=       sum(UpperCAmelCase__ )
														totals_frequencies[total] += 1

							return totals_frequencies




def 							lowerCamelCase	(      )			->      float:
							lowercase_					:			Optional[Any]										=       total_frequency_distribution(
							    sides_number=4      ,      dice_number=9 )
							lowercase_					:			List[str]										=       total_frequency_distribution(
							    sides_number=6      ,      dice_number=6 )

							lowercase_					:			Union[str, Any]										=       0
							lowercase_					:			Tuple										=       9
							lowercase_					:			Optional[int]										=       4 * 9
							lowercase_					:			List[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] )

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

							lowercase_					:			Dict										=       round(UpperCAmelCase__      ,      ndigits=7 )

							return rounded_peter_win_probability


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





