


from itertools import product
def      snake_case_						( __lowercase			,       __lowercase       ):
   UpperCAmelCase_							:      Dict						=   sides_number
   UpperCAmelCase_							:      Optional[Any]						=   max_face_number * dice_number
   UpperCAmelCase_							:      str						=   [0] * (max_total + 1)

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

   return totals_frequencies
def      snake_case_						( ):
   UpperCAmelCase_							:      Optional[Any]						=   total_frequency_distribution(
       sides_number=4			,       dice_number=9       )
   UpperCAmelCase_							:      Optional[int]						=   total_frequency_distribution(
       sides_number=6			,       dice_number=6       )

   UpperCAmelCase_							:      Optional[Any]						=   0
   UpperCAmelCase_							:      Any						=   9
   UpperCAmelCase_							:      Union[str, Any]						=   4 * 9
   UpperCAmelCase_							:      Optional[Any]						=   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_							:      Union[str, Any]						=   (4**9) * (6**6)
   UpperCAmelCase_							:      List[str]						=   peter_wins_count / total_games_number

   UpperCAmelCase_							:      Dict						=   round(_lowerCamelCase			,       ndigits=7       )

   return rounded_peter_win_probability


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






from ...configuration_utils import PretrainedConfig
from ...utils import logging


__UpperCamelCase				:  Any      					=							logging.get_logger(__name__)

__UpperCamelCase				:  Dict      					=							{
    'bigcode/gpt_bigcode-santacoder': 'https://huggingface.co/bigcode/gpt_bigcode-santacoder/resolve/main/config.json',
}





class  lowerCAmelCase__(    snake_case__						):






    '''simple docstring'''





    A_  :     List[str]			= 'gpt_bigcode'
    A_  :     Optional[Any]			= ['past_key_values']
    A_  :     Optional[int]			= {
        'hidden_size': 'n_embd',
        'max_position_embeddings': 'n_positions',
        'num_attention_heads': 'n_head',
        'num_hidden_layers': 'n_layer',
    }





    def __init__(	self				:   int       ,   __snake_case				:   Dict=50_257       ,   __snake_case				:   List[str]=1_024       ,   __snake_case				:   Dict=768       ,   __snake_case				:   Optional[int]=12       ,   __snake_case				:   str=12       ,   __snake_case				:   List[str]=None       ,   __snake_case				:   List[str]="gelu_pytorch_tanh"       ,   __snake_case				:   Optional[Any]=0.1       ,   __snake_case				:   str=0.1       ,   __snake_case				:   Optional[Any]=0.1       ,   __snake_case				:   List[str]=1E-5       ,   __snake_case				:   Dict=0.02       ,   __snake_case				:   Optional[int]=True       ,   __snake_case				:   Tuple=True       ,   __snake_case				:   Optional[Any]=50_256       ,   __snake_case				:   Optional[Any]=50_256       ,   __snake_case				:   Optional[Any]=True       ,   __snake_case				:   Optional[Any]=True       ,   __snake_case				:   List[Any]=True       ,   **__snake_case				:   List[str]       ,   ):





       '''simple docstring'''
       UpperCAmelCase_							:      Any						=   vocab_size
       UpperCAmelCase_							:      int						=   n_positions
       UpperCAmelCase_							:      Any						=   n_embd
       UpperCAmelCase_							:      Union[str, Any]						=   n_layer
       UpperCAmelCase_							:      List[str]						=   n_head
       UpperCAmelCase_							:      List[Any]						=   n_inner
       UpperCAmelCase_							:      Optional[int]						=   activation_function
       UpperCAmelCase_							:      str						=   resid_pdrop
       UpperCAmelCase_							:      Optional[Any]						=   embd_pdrop
       UpperCAmelCase_							:      str						=   attn_pdrop
       UpperCAmelCase_							:      Any						=   layer_norm_epsilon
       UpperCAmelCase_							:      List[str]						=   initializer_range
       UpperCAmelCase_							:      Optional[int]						=   scale_attn_weights
       UpperCAmelCase_							:      Union[str, Any]						=   use_cache
       UpperCAmelCase_							:      Dict						=   attention_softmax_in_fpaa
       UpperCAmelCase_							:      Union[str, Any]						=   scale_attention_softmax_in_fpaa
       UpperCAmelCase_							:      Optional[int]						=   multi_query

       UpperCAmelCase_							:      Optional[Any]						=   bos_token_id
       UpperCAmelCase_							:      Tuple						=   eos_token_id

       super().__init__(bos_token_id=__snake_case       ,   eos_token_id=__snake_case       ,   **__snake_case	)