



'''simple docstring'''


def 			UpperCAmelCase_							(		lowercase__ = 2_0							):


     '''simple docstring'''







     try:
          a_									=int(lowercase__							)
     except (TypeError, ValueError):
          raise TypeError("Parameter n must be int or castable to int."							)
     if n <= 0:
          raise ValueError("Parameter n must be greater than or equal to one."							)
     a_									=0
     while 1:
          i += n * (n - 1)
          a_									=0
          for j in range(2							,						lowercase__							):
               if i % j != 0:
                    a_									=1
                    break
          if nfound == 0:
               if i == 0:
                    a_									=1
               return i
     return None


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







'''simple docstring'''


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

from ... import PreTrainedTokenizer, TensorType, is_torch_available
from ...configuration_utils import PretrainedConfig
from ...onnx import OnnxConfigWithPast, PatchingSpec
from ...utils import logging


lowercase											=      logging.get_logger(__name__)

lowercase											=      {
    '''gpt2''': '''https://huggingface.co/gpt2/resolve/main/config.json''',
    '''gpt2-medium''': '''https://huggingface.co/gpt2-medium/resolve/main/config.json''',
    '''gpt2-large''': '''https://huggingface.co/gpt2-large/resolve/main/config.json''',
    '''gpt2-xl''': '''https://huggingface.co/gpt2-xl/resolve/main/config.json''',
    '''distilgpt2''': '''https://huggingface.co/distilgpt2/resolve/main/config.json''',
}







class 						UpperCAmelCase						(		__a):


 '''simple docstring'''




 __magic_name__       :			str	=   "gpt2"
 __magic_name__       :			str	=   ["past_key_values"]
 __magic_name__       :			Dict	=   {
     "hidden_size": "n_embd",
     "max_position_embeddings": "n_positions",
     "num_attention_heads": "n_head",
     "num_hidden_layers": "n_layer",
 }




 def __init__( self				,	lowerCAmelCase_=5_0_2_5_7				,	lowerCAmelCase_=1_0_2_4				,	lowerCAmelCase_=7_6_8				,	lowerCAmelCase_=1_2				,	lowerCAmelCase_=1_2				,	lowerCAmelCase_=None				,	lowerCAmelCase_="gelu_new"				,	lowerCAmelCase_=0.1				,	lowerCAmelCase_=0.1				,	lowerCAmelCase_=0.1				,	lowerCAmelCase_=1e-5				,	lowerCAmelCase_=0.0_2				,	lowerCAmelCase_="cls_index"				,	lowerCAmelCase_=True				,	lowerCAmelCase_=None				,	lowerCAmelCase_=True				,	lowerCAmelCase_=0.1				,	lowerCAmelCase_=True				,	lowerCAmelCase_=True				,	lowerCAmelCase_=5_0_2_5_6				,	lowerCAmelCase_=5_0_2_5_6				,	lowerCAmelCase_=False				,	lowerCAmelCase_=False				,	**lowerCAmelCase_				,	)			->   Dict:



      """simple docstring"""







      a_									=vocab_size
      a_									=n_positions
      a_									=n_embd
      a_									=n_layer
      a_									=n_head
      a_									=n_inner
      a_									=activation_function
      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
      a_									=scale_attn_weights
      a_									=use_cache
      a_									=scale_attn_by_inverse_layer_idx
      a_									=reorder_and_upcast_attn

      a_									=bos_token_id
      a_									=eos_token_id

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







class 						UpperCAmelCase						(		__a):


 '''simple docstring'''




 def __init__( self				,	lowerCAmelCase_				,	lowerCAmelCase_ = "default"				,	lowerCAmelCase_ = None				,	lowerCAmelCase_ = False				,	)			->   List[str]:



      """simple docstring"""







      super().__init__(lowerCAmelCase_				,	task=lowerCAmelCase_				,	patching_specs=lowerCAmelCase_				,	use_past=lowerCAmelCase_)
      if not getattr(self._config				,	"pad_token_id"				,	lowerCAmelCase_):
           # TODO: how to do that better?
           a_									=0




 @property
 def    lowercase_	( self)			->   Mapping[str, Mapping[int, str]]:



      """simple docstring"""







      a_									=OrderedDict({"input_ids": {0: "batch", 1: "sequence"}})
      if self.use_past:
           self.fill_with_past_key_values_(lowerCAmelCase_				,	direction="inputs")
           a_									={0: "batch", 1: "past_sequence + sequence"}
      else:
           a_									={0: "batch", 1: "sequence"}

      return common_inputs




 @property
 def    lowercase_	( self)			->   int:



      """simple docstring"""







      return self._config.n_layer




 @property
 def    lowercase_	( self)			->   int:



      """simple docstring"""







      return self._config.n_head




 def    lowercase_	( self				,	lowerCAmelCase_				,	lowerCAmelCase_ = -1				,	lowerCAmelCase_ = -1				,	lowerCAmelCase_ = False				,	lowerCAmelCase_ = None				,	)			->   Mapping[str, Any]:



      """simple docstring"""







      a_									=super(lowerCAmelCase_				,	self).generate_dummy_inputs(
          lowerCAmelCase_				,	batch_size=lowerCAmelCase_				,	seq_length=lowerCAmelCase_				,	is_pair=lowerCAmelCase_				,	framework=lowerCAmelCase_)

      # We need to order the input in the way they appears in the forward()
      a_									=OrderedDict({"input_ids": common_inputs["input_ids"]})

      # Need to add the past_keys
      if self.use_past:
           if not is_torch_available():
                raise ValueError("Cannot generate dummy past_keys inputs without PyTorch installed.")
           else:
                import torch

                a_		,    a_									=common_inputs["input_ids"].shape
                # Not using the same length for past_key_values
                a_									=seqlen + 2
                a_									=(
                    batch,
                    self.num_attention_heads,
                    past_key_values_length,
                    self._config.hidden_size // self.num_attention_heads,
                )
                a_									=[
                    (torch.zeros(lowerCAmelCase_), torch.zeros(lowerCAmelCase_)) for _ in range(self.num_layers)
                ]

      a_									=common_inputs["attention_mask"]
      if self.use_past:
           a_									=ordered_inputs["attention_mask"].dtype
           a_									=torch.cat(
               [ordered_inputs["attention_mask"], torch.ones(lowerCAmelCase_				,	lowerCAmelCase_				,	dtype=lowerCAmelCase_)]				,	dim=1)

      return ordered_inputs




 @property
 def    lowercase_	( self)			->   int:



      """simple docstring"""







      return 1_3


