



'''simple docstring'''






from itertools import product
def    lowerCamelCase__ (		_A				,    _A       ):
  a		:      int       =  sides_number
  a		:      Tuple       =  max_face_number * dice_number
  a		:      str       =  [0] * (max_total + 1)

  a		:      Optional[Any]       =  1
  a		:      List[Any]       =  range(_A				,    max_face_number + 1       )
  for dice_numbers in product(_A				,    repeat=_A       ):
    a		:      Any       =  sum(_A       )
    totals_frequencies[total] += 1

  return totals_frequencies
def    lowerCamelCase__ (		):
  a		:      List[Any]       =  total_frequency_distribution(
      sides_number=4				,    dice_number=9       )
  a		:      Dict       =  total_frequency_distribution(
      sides_number=6				,    dice_number=6       )

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

  a		:      List[str]       =  (4**9) * (6**6)
  a		:      Tuple       =  peter_wins_count / total_games_number

  a		:      Optional[Any]       =  round(_A				,    ndigits=7       )

  return rounded_peter_win_probability


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




'''simple docstring'''






from collections import OrderedDict
from typing import TYPE_CHECKING, Any, Mapping, Optional

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


if TYPE_CHECKING:
     from ... import FeatureExtractionMixin, TensorType

lowerCAmelCase:      List[Any]		 =		logging.get_logger(__name__)

lowerCAmelCase:      List[str]		 =		{
    'openai/imagegpt-small': '',
    'openai/imagegpt-medium': '',
    'openai/imagegpt-large': '',
}

class 							a__(      lowerCamelCase__			):
    lowercase__				=					"""imagegpt"""
    lowercase__				=					["""past_key_values"""]
    lowercase__				=					{
        """hidden_size""": """n_embd""",
        """max_position_embeddings""": """n_positions""",
        """num_attention_heads""": """n_head""",
        """num_hidden_layers""": """n_layer""",
    }







    def __init__(   self				:						List[str]		,    __snake_case				:						int=5_12 + 1		,    __snake_case				:						Optional[Any]=32 * 32		,    __snake_case				:						Optional[Any]=5_12		,    __snake_case				:						List[str]=24		,    __snake_case				:						Tuple=8		,    __snake_case				:						Optional[int]=None		,    __snake_case				:						Dict="quick_gelu"		,    __snake_case				:						Dict=0.1		,    __snake_case				:						List[str]=0.1		,    __snake_case				:						Optional[Any]=0.1		,    __snake_case				:						Tuple=1e-5		,    __snake_case				:						Union[str, Any]=0.02		,    __snake_case				:						Optional[int]=True		,    __snake_case				:						Dict=True		,    __snake_case				:						str=False		,    __snake_case				:						Any=False		,    __snake_case				:						List[Any]=False		,    **__snake_case				:						List[str]		,    ):
      a		:      Optional[Any]       =  vocab_size
      a		:      Union[str, Any]       =  n_positions
      a		:      int       =  n_embd
      a		:      int       =  n_layer
      a		:      str       =  n_head
      a		:      int       =  n_inner
      a		:      int       =  activation_function
      a		:      Any       =  resid_pdrop
      a		:      Tuple       =  embd_pdrop
      a		:      List[Any]       =  attn_pdrop
      a		:      Tuple       =  layer_norm_epsilon
      a		:      Any       =  initializer_range
      a		:      str       =  scale_attn_weights
      a		:      List[Any]       =  use_cache
      a		:      Any       =  scale_attn_by_inverse_layer_idx
      a		:      Optional[Any]       =  reorder_and_upcast_attn
      a		:      str       =  tie_word_embeddings

      super().__init__(tie_word_embeddings=__snake_case		,    **__snake_case			)

class 							a__(      lowerCamelCase__			):







    @property
    def     lowercase_ (   self				:						Union[str, Any]			):
      return OrderedDict(
          [
              ('input_ids', {0: 'batch', 1: 'sequence'}),
          ]			)







    def     lowercase_ (   self				:						Union[str, Any]		,    __snake_case				:						"FeatureExtractionMixin"		,    __snake_case				:						int = 1		,    __snake_case				:						int = -1		,    __snake_case				:						bool = False		,    __snake_case				:						Optional["TensorType"] = None		,    __snake_case				:						int = 3		,    __snake_case				:						int = 32		,    __snake_case				:						int = 32		,    ):
      a		:      Dict       =  self._generate_dummy_images(__snake_case		,    __snake_case		,    __snake_case		,    __snake_case			)
      a		:      Union[str, Any]       =  dict(preprocessor(images=__snake_case		,    return_tensors=__snake_case			)			)

      return inputs