





"""simple docstring"""



from itertools import product







def 		__lowercase     (   snake_case_  :  int				,snake_case_  :  int						)   ->list[int]:



    '''simple docstring'''







    __A    :						int						 =     sides_number
    __A    :						Any						 =     max_face_number * dice_number
    __A    :						List[Any]						 =     [0] * (max_total + 1)

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

    return totals_frequencies







def 		__lowercase     (   )   ->float:



    '''simple docstring'''







    __A    :						Tuple						 =     total_frequency_distribution(
        sides_number=4				,dice_number=9						)
    __A    :						Any						 =     total_frequency_distribution(
        sides_number=6				,dice_number=6						)

    __A    :						Any						 =     0
    __A    :						str						 =     9
    __A    :						Optional[int]						 =     4 * 9
    __A    :						Optional[int]						 =     6
    for peter_total in range(snake_case_				,max_peter_total + 1						):
        peter_wins_count += peter_totals_frequencies[peter_total] * sum(
            colin_totals_frequencies[min_colin_total:peter_total]						)

    __A    :						int						 =     (4**9) * (6**6)
    __A    :						str						 =     peter_wins_count / total_games_number

    __A    :						Tuple						 =     round(snake_case_				,ndigits=7						)

    return rounded_peter_win_probability


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











"""simple docstring"""



from collections import OrderedDict
from typing import Mapping

from ...configuration_utils import PretrainedConfig
from ...onnx import OnnxConfig
from ...utils import logging


a_ =			logging.get_logger(__name__)

a_ =			{
    """bert-base-uncased""": """https://huggingface.co/bert-base-uncased/resolve/main/config.json""",
    """bert-large-uncased""": """https://huggingface.co/bert-large-uncased/resolve/main/config.json""",
    """bert-base-cased""": """https://huggingface.co/bert-base-cased/resolve/main/config.json""",
    """bert-large-cased""": """https://huggingface.co/bert-large-cased/resolve/main/config.json""",
    """bert-base-multilingual-uncased""": """https://huggingface.co/bert-base-multilingual-uncased/resolve/main/config.json""",
    """bert-base-multilingual-cased""": """https://huggingface.co/bert-base-multilingual-cased/resolve/main/config.json""",
    """bert-base-chinese""": """https://huggingface.co/bert-base-chinese/resolve/main/config.json""",
    """bert-base-german-cased""": """https://huggingface.co/bert-base-german-cased/resolve/main/config.json""",
    """bert-large-uncased-whole-word-masking""": (
        """https://huggingface.co/bert-large-uncased-whole-word-masking/resolve/main/config.json"""
    ),
    """bert-large-cased-whole-word-masking""": (
        """https://huggingface.co/bert-large-cased-whole-word-masking/resolve/main/config.json"""
    ),
    """bert-large-uncased-whole-word-masking-finetuned-squad""": (
        """https://huggingface.co/bert-large-uncased-whole-word-masking-finetuned-squad/resolve/main/config.json"""
    ),
    """bert-large-cased-whole-word-masking-finetuned-squad""": (
        """https://huggingface.co/bert-large-cased-whole-word-masking-finetuned-squad/resolve/main/config.json"""
    ),
    """bert-base-cased-finetuned-mrpc""": """https://huggingface.co/bert-base-cased-finetuned-mrpc/resolve/main/config.json""",
    """bert-base-german-dbmdz-cased""": """https://huggingface.co/bert-base-german-dbmdz-cased/resolve/main/config.json""",
    """bert-base-german-dbmdz-uncased""": """https://huggingface.co/bert-base-german-dbmdz-uncased/resolve/main/config.json""",
    """cl-tohoku/bert-base-japanese""": """https://huggingface.co/cl-tohoku/bert-base-japanese/resolve/main/config.json""",
    """cl-tohoku/bert-base-japanese-whole-word-masking""": (
        """https://huggingface.co/cl-tohoku/bert-base-japanese-whole-word-masking/resolve/main/config.json"""
    ),
    """cl-tohoku/bert-base-japanese-char""": (
        """https://huggingface.co/cl-tohoku/bert-base-japanese-char/resolve/main/config.json"""
    ),
    """cl-tohoku/bert-base-japanese-char-whole-word-masking""": (
        """https://huggingface.co/cl-tohoku/bert-base-japanese-char-whole-word-masking/resolve/main/config.json"""
    ),
    """TurkuNLP/bert-base-finnish-cased-v1""": (
        """https://huggingface.co/TurkuNLP/bert-base-finnish-cased-v1/resolve/main/config.json"""
    ),
    """TurkuNLP/bert-base-finnish-uncased-v1""": (
        """https://huggingface.co/TurkuNLP/bert-base-finnish-uncased-v1/resolve/main/config.json"""
    ),
    """wietsedv/bert-base-dutch-cased""": """https://huggingface.co/wietsedv/bert-base-dutch-cased/resolve/main/config.json""",
    # See all BERT models at https://huggingface.co/models?filter=bert
}






class 		__snake_case					(		SCREAMING_SNAKE_CASE__     ):





 """simple docstring"""


 _lowerCamelCase        =     """bert"""

 def __init__(    self					,						__lowerCamelCase=3_0522					,						__lowerCamelCase=768					,						__lowerCamelCase=12					,						__lowerCamelCase=12					,						__lowerCamelCase=3072					,						__lowerCamelCase="gelu"					,						__lowerCamelCase=0.1					,						__lowerCamelCase=0.1					,						__lowerCamelCase=512					,						__lowerCamelCase=2					,						__lowerCamelCase=0.0_2					,						__lowerCamelCase=1e-1_2					,						__lowerCamelCase=0					,						__lowerCamelCase="absolute"					,						__lowerCamelCase=True					,						__lowerCamelCase=None					,						**__lowerCamelCase					,						):



     '''simple docstring'''




     super().__init__(pad_token_id=__lowerCamelCase					,						**__lowerCamelCase  )

     __A    :						Dict						 =     vocab_size
     __A    :						Any						 =     hidden_size
     __A    :						str						 =     num_hidden_layers
     __A    :						int						 =     num_attention_heads
     __A    :						Optional[int]						 =     hidden_act
     __A    :						List[Any]						 =     intermediate_size
     __A    :						Tuple						 =     hidden_dropout_prob
     __A    :						Optional[int]						 =     attention_probs_dropout_prob
     __A    :						Optional[int]						 =     max_position_embeddings
     __A    :						Optional[Any]						 =     type_vocab_size
     __A    :						Optional[Any]						 =     initializer_range
     __A    :						Dict						 =     layer_norm_eps
     __A    :						Any						 =     position_embedding_type
     __A    :						Optional[int]						 =     use_cache
     __A    :						str						 =     classifier_dropout






class 		__snake_case					(		SCREAMING_SNAKE_CASE__     ):





 """simple docstring"""


 @property
 def 					UpperCamelCase__(    self  ):



     '''simple docstring'''




     if self.task == "multiple-choice":
         __A    :						str						 =     {0: '''batch''', 1: '''choice''', 2: '''sequence'''}
     else:
         __A    :						Tuple						 =     {0: '''batch''', 1: '''sequence'''}
     return OrderedDict(
         [
             ('''input_ids''', dynamic_axis),
             ('''attention_mask''', dynamic_axis),
             ('''token_type_ids''', dynamic_axis),
         ]  )




