



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


__snake_case     :List[str]			       =logging.get_logger(__name__)

__snake_case     :int			       ={'openai-gpt': 'https://huggingface.co/openai-gpt/resolve/main/config.json'}



class        lowerCAmelCase__					(  _lowerCamelCase       ):
				A_   :     Optional[Any]								=     'openai-gpt'
				A_   :     Any								=     {
				    'max_position_embeddings': 'n_positions',
				    'hidden_size': 'n_embd',
				    'num_attention_heads': 'n_head',
				    'num_hidden_layers': 'n_layer',
				}


				def __init__(							self      :  List[Any]						, __UpperCamelCase      :  List[str]=40_478						, __UpperCamelCase      :  List[Any]=512						, __UpperCamelCase      :  List[Any]=768						, __UpperCamelCase      :  Optional[int]=12						, __UpperCamelCase      :  Dict=12						, __UpperCamelCase      :  List[str]="gelu"						, __UpperCamelCase      :  str=0.1						, __UpperCamelCase      :  Optional[Any]=0.1						, __UpperCamelCase      :  Union[str, Any]=0.1						, __UpperCamelCase      :  List[str]=1e-5						, __UpperCamelCase      :  List[Any]=0.0_2						, __UpperCamelCase      :  str="cls_index"						, __UpperCamelCase      :  int=True						, __UpperCamelCase      :  int=None						, __UpperCamelCase      :  Optional[int]=True						, __UpperCamelCase      :  Tuple=0.1						, **__UpperCamelCase      :  List[Any]						, )		->     List[str]:
											A      						=    vocab_size
											A      						=    n_positions
											A      						=    n_embd
											A      						=    n_layer
											A      						=    n_head
											A      						=    afn
											A      						=    resid_pdrop
											A      						=    embd_pdrop
											A      						=    attn_pdrop
											A      						=    layer_norm_epsilon
											A      						=    initializer_range
											A      						=    summary_type
											A      						=    summary_use_proj
											A      						=    summary_activation
											A      						=    summary_first_dropout
											A      						=    summary_proj_to_labels
											super().__init__(**__UpperCamelCase       )

'''simple docstring'''

from math import factorial

snake_case									=    {str(digit): factorial(digit) for digit in range(10)}


def        UpperCAmelCase_ (  lowerCamelCase_			):







 """simple docstring"""


 if not isinstance(lowerCamelCase_      ,			lowerCamelCase_			):
  raise TypeError("Parameter number must be int"			)

 if number < 0:
  raise ValueError("Parameter number must be greater than or equal to 0"			)

 # Converts number in string to iterate on its digits and adds its factorial.
 return sum(DIGIT_FACTORIAL[digit] for digit in str(lowerCamelCase_			)			)


def        UpperCAmelCase_ (  lowerCamelCase_ = 6_0      ,			lowerCamelCase_ = 1_0_0_0_0_0_0			):







 """simple docstring"""


 if not isinstance(lowerCamelCase_      ,			lowerCamelCase_			) or not isinstance(lowerCamelCase_      ,			lowerCamelCase_			):
  raise TypeError("Parameters chain_length and number_limit must be int"			)

 if chain_length <= 0 or number_limit <= 0:
  raise ValueError(
      "Parameters chain_length and number_limit must be greater than 0"			)

 # the counter for the chains with the exact desired length
 lowerCAmelCase__     :   str     		=	0
 # the cached sizes of the previous chains
 lowerCAmelCase__     :   dict[int, int]     		=	{}

 for start_chain_element in range(1      ,			lowerCamelCase_			):
  # The temporary set will contain the elements of the chain
  lowerCAmelCase__     :   Any     		=	set()
  lowerCAmelCase__     :   int     		=	0

  # Stop computing the chain when you find a cached size, a repeating item or the
  # length is greater then the desired one.
  lowerCAmelCase__     :   Dict     		=	start_chain_element
  while (
      chain_element not in chain_sets_lengths
      and chain_element not in chain_set
      and chain_set_length <= chain_length
  ):
   chain_set.add(lowerCamelCase_			)
   chain_set_length += 1
   lowerCAmelCase__     :   Dict     		=	digit_factorial_sum(lowerCamelCase_			)

  if chain_element in chain_sets_lengths:
   chain_set_length += chain_sets_lengths[chain_element]

  lowerCAmelCase__     :   Optional[Any]     		=	chain_set_length

  # If chain contains the exact amount of elements increase the counter
  if chain_set_length == chain_length:
   chains_counter += 1

 return chains_counter


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     print(f'{solution()}')





