


'''simple docstring'''
from itertools import product





def    a__			(   lowerCAmelCase__    ,   lowerCAmelCase__		)       ->      list[int]:
    UpperCAmelCase__     :						Optional[Any]						=							sides_number
    UpperCAmelCase__     :						Optional[Any]						=							max_face_number * dice_number
    UpperCAmelCase__     :						Optional[int]						=							[0] * (max_total + 1)

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

    return totals_frequencies





def    a__			(   )       ->      float:
    UpperCAmelCase__     :						int						=							total_frequency_distribution(
        sides_number=4    ,   dice_number=9		)
    UpperCAmelCase__     :						Optional[int]						=							total_frequency_distribution(
        sides_number=6    ,   dice_number=6		)

    UpperCAmelCase__     :						Union[str, Any]						=							0
    UpperCAmelCase__     :						str						=							9
    UpperCAmelCase__     :						str						=							4 * 9
    UpperCAmelCase__     :						Tuple						=							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]		)

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

    UpperCAmelCase__     :						Any						=							round(lowerCAmelCase__    ,   ndigits=7		)

    return rounded_peter_win_probability


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







import warnings

from ...utils import logging
from .image_processing_yolos import YolosImageProcessor


_lowercase		:  int			       =logging.get_logger(__name__)






class 						UpperCamelCase_  (  snake_case__							):



					def __init__(		self     :     Tuple       ,      *lowerCamelCase     :     List[Any]       ,      **lowerCamelCase     :     Union[str, Any]						):
							warnings.warn(
							    'The class YolosFeatureExtractor is deprecated and will be removed in version 5 of Transformers. Please'
							    ' use YolosImageProcessor instead.'       ,      lowerCamelCase       ,      )
							super().__init__(*lowerCamelCase       ,      **lowerCamelCase						)
