

"""simple docstring"""
from itertools import product




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

      UpperCAmelCase__       :				int						 =  1
      UpperCAmelCase__       :				Tuple						 =  range(_UpperCAmelCase       ,     max_face_number + 1  )
      for dice_numbers in product(_UpperCAmelCase       ,     repeat=_UpperCAmelCase  ):
            UpperCAmelCase__       :				int						 =  sum(_UpperCAmelCase  )
            totals_frequencies[total] += 1

      return totals_frequencies




def  a__		(		)     ->      int:
      UpperCAmelCase__       :				str						 =  total_frequency_distribution(
          sides_number=4       ,     dice_number=9  )
      UpperCAmelCase__       :				Any						 =  total_frequency_distribution(
          sides_number=6       ,     dice_number=6  )

      UpperCAmelCase__       :				List[str]						 =  0
      UpperCAmelCase__       :				Tuple						 =  9
      UpperCAmelCase__       :				List[Any]						 =  4 * 9
      UpperCAmelCase__       :				Dict						 =  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]  )

      UpperCAmelCase__       :				Optional[int]						 =  (4**9) * (6**6)
      UpperCAmelCase__       :				Optional[Any]						 =  peter_wins_count / total_games_number

      UpperCAmelCase__       :				str						 =  round(_UpperCAmelCase       ,     ndigits=7  )

      return rounded_peter_win_probability


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






from typing import Dict, List, Optional, Union

import numpy as np

from ...image_processing_utils import BaseImageProcessor, BatchFeature, get_size_dict
from ...image_transforms import (
    center_crop,
    convert_to_rgb,
    get_resize_output_image_size,
    normalize,
    rescale,
    resize,
    to_channel_dimension_format,
)
from ...image_utils import (
    OPENAI_CLIP_MEAN,
    OPENAI_CLIP_STD,
    ChannelDimension,
    ImageInput,
    PILImageResampling,
    make_list_of_images,
    to_numpy_array,
    valid_images,
)
from ...utils import TensorType, is_vision_available, logging


__A   			=logging.get_logger(__name__)


if is_vision_available():
				import PIL

class 		UpperCAmelCase__			(			__UpperCamelCase   ):




			'''simple docstring'''






			UpperCamelCase									=       ["""pixel_values"""]




			def __init__(   self							: Tuple       ,       a_							: bool = True       ,       a_							: Dict[str, int] = None       ,       a_							: PILImageResampling = PILImageResampling.BICUBIC       ,       a_							: bool = True       ,       a_							: Dict[str, int] = None       ,       a_							: bool = True       ,       a_							: Union[int, float] = 1 / 2_55       ,       a_							: bool = True       ,       a_							: Optional[Union[float, List[float]]] = None       ,       a_							: Optional[Union[float, List[float]]] = None       ,       a_							: bool = True       ,       **a_							: str       ,       ):
					'''simple docstring'''





					super().__init__(**a_ )
					__UpperCAmelCase    :     List[Any]													=	size if size is not None else {'''shortest_edge''': 2_24}
					__UpperCAmelCase    :     List[str]													=	get_size_dict(a_       ,       default_to_square=a_ )
					__UpperCAmelCase    :     int													=	crop_size if crop_size is not None else {'''height''': 2_24, '''width''': 2_24}
					__UpperCAmelCase    :     Optional[int]													=	get_size_dict(a_       ,       default_to_square=a_       ,       param_name='''crop_size''' )

					__UpperCAmelCase    :     int													=	do_resize
					__UpperCAmelCase    :     Union[str, Any]													=	size
					__UpperCAmelCase    :     Union[str, Any]													=	resample
					__UpperCAmelCase    :     Any													=	do_center_crop
					__UpperCAmelCase    :     Any													=	crop_size
					__UpperCAmelCase    :     Any													=	do_rescale
					__UpperCAmelCase    :     Dict													=	rescale_factor
					__UpperCAmelCase    :     Union[str, Any]													=	do_normalize
					__UpperCAmelCase    :     Any													=	image_mean if image_mean is not None else OPENAI_CLIP_MEAN
					__UpperCAmelCase    :     int													=	image_std if image_std is not None else OPENAI_CLIP_STD
					__UpperCAmelCase    :     List[str]													=	do_convert_rgb




			def  snake_case__     (   self							: Optional[Any]       ,       a_							: np.ndarray       ,       a_							: Dict[str, int]       ,       a_							: PILImageResampling = PILImageResampling.BICUBIC       ,       a_							: Optional[Union[str, ChannelDimension]] = None       ,       **a_							: Optional[int]       ,       ):
					'''simple docstring'''





					__UpperCAmelCase    :     Dict													=	get_size_dict(a_       ,       default_to_square=a_ )
					if "shortest_edge" not in size:
							raise ValueError(F'The `size` parameter must contain the key `shortest_edge`. Got {size.keys()}' )
					__UpperCAmelCase    :     Optional[int]													=	get_resize_output_image_size(a_       ,       size=size['''shortest_edge''']       ,       default_to_square=a_ )
					return resize(a_       ,       size=a_       ,       resample=a_       ,       data_format=a_       ,       **a_ )




			def  snake_case__     (   self							: Union[str, Any]       ,       a_							: np.ndarray       ,       a_							: Dict[str, int]       ,       a_							: Optional[Union[str, ChannelDimension]] = None       ,       **a_							: Dict       ,       ):
					'''simple docstring'''





					__UpperCAmelCase    :     Optional[Any]													=	get_size_dict(a_ )
					if "height" not in size or "width" not in size:
							raise ValueError(F'The `size` parameter must contain the keys (height, width). Got {size.keys()}' )
					return center_crop(a_       ,       size=(size['''height'''], size['''width'''])       ,       data_format=a_       ,       **a_ )




			def  snake_case__     (   self							: Union[str, Any]       ,       a_							: np.ndarray       ,       a_							: Union[int, float]       ,       a_							: Optional[Union[str, ChannelDimension]] = None       ,       **a_							: List[str]       ,       ):
					'''simple docstring'''





					return rescale(a_       ,       scale=a_       ,       data_format=a_       ,       **a_ )




			def  snake_case__     (   self							: Optional[Any]       ,       a_							: np.ndarray       ,       a_							: Union[float, List[float]]       ,       a_							: Union[float, List[float]]       ,       a_							: Optional[Union[str, ChannelDimension]] = None       ,       **a_							: Dict       ,       ):
					'''simple docstring'''





					return normalize(a_       ,       mean=a_       ,       std=a_       ,       data_format=a_       ,       **a_ )




			def  snake_case__     (   self							: Any       ,       a_							: ImageInput       ,       a_							: bool = None       ,       a_							: Dict[str, int] = None       ,       a_							: PILImageResampling = None       ,       a_							: bool = None       ,       a_							: int = None       ,       a_							: bool = None       ,       a_							: float = None       ,       a_							: bool = None       ,       a_							: Optional[Union[float, List[float]]] = None       ,       a_							: Optional[Union[float, List[float]]] = None       ,       a_							: bool = None       ,       a_							: Optional[Union[str, TensorType]] = None       ,       a_							: Optional[ChannelDimension] = ChannelDimension.FIRST       ,       **a_							: Dict       ,       ):
					'''simple docstring'''





					__UpperCAmelCase    :     Tuple													=	do_resize if do_resize is not None else self.do_resize
					__UpperCAmelCase    :     Optional[Any]													=	size if size is not None else self.size
					__UpperCAmelCase    :     Dict													=	get_size_dict(a_       ,       param_name='''size'''       ,       default_to_square=a_ )
					__UpperCAmelCase    :     int													=	resample if resample is not None else self.resample
					__UpperCAmelCase    :     Optional[Any]													=	do_center_crop if do_center_crop is not None else self.do_center_crop
					__UpperCAmelCase    :     Any													=	crop_size if crop_size is not None else self.crop_size
					__UpperCAmelCase    :     Dict													=	get_size_dict(a_       ,       param_name='''crop_size'''       ,       default_to_square=a_ )
					__UpperCAmelCase    :     int													=	do_rescale if do_rescale is not None else self.do_rescale
					__UpperCAmelCase    :     Optional[int]													=	rescale_factor if rescale_factor is not None else self.rescale_factor
					__UpperCAmelCase    :     List[str]													=	do_normalize if do_normalize is not None else self.do_normalize
					__UpperCAmelCase    :     Optional[int]													=	image_mean if image_mean is not None else self.image_mean
					__UpperCAmelCase    :     Tuple													=	image_std if image_std is not None else self.image_std
					__UpperCAmelCase    :     List[str]													=	do_convert_rgb if do_convert_rgb is not None else self.do_convert_rgb

					__UpperCAmelCase    :     List[str]													=	make_list_of_images(a_ )

					if not valid_images(a_ ):
							raise ValueError(
							    '''Invalid image type. Must be of type PIL.Image.Image, numpy.ndarray, '''
							    '''torch.Tensor, tf.Tensor or jax.ndarray.''' )

					if do_resize and size is None:
							raise ValueError('''Size must be specified if do_resize is True.''' )

					if do_center_crop and crop_size is None:
							raise ValueError('''Crop size must be specified if do_center_crop is True.''' )

					if do_rescale and rescale_factor is None:
							raise ValueError('''Rescale factor must be specified if do_rescale is True.''' )

					if do_normalize and (image_mean is None or image_std is None):
							raise ValueError('''Image mean and std must be specified if do_normalize is True.''' )

					# PIL RGBA images are converted to RGB
					if do_convert_rgb:
							__UpperCAmelCase    :     Optional[Any]													=	[convert_to_rgb(a_ ) for image in images]

					# All transformations expect numpy arrays.
					__UpperCAmelCase    :     int													=	[to_numpy_array(a_ ) for image in images]

					if do_resize:
							__UpperCAmelCase    :     int													=	[self.resize(image=a_       ,       size=a_       ,       resample=a_ ) for image in images]

					if do_center_crop:
							__UpperCAmelCase    :     List[str]													=	[self.center_crop(image=a_       ,       size=a_ ) for image in images]

					if do_rescale:
							__UpperCAmelCase    :     Dict													=	[self.rescale(image=a_       ,       scale=a_ ) for image in images]

					if do_normalize:
							__UpperCAmelCase    :     Optional[int]													=	[self.normalize(image=a_       ,       mean=a_       ,       std=a_ ) for image in images]

					__UpperCAmelCase    :     Optional[int]													=	[to_channel_dimension_format(a_       ,       a_ ) for image in images]

					__UpperCAmelCase    :     Union[str, Any]													=	{'''pixel_values''': images}
					return BatchFeature(data=a_       ,       tensor_type=a_ )





