
"""simple docstring"""




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

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


A__      :	Any          =    logging.get_logger(__name__)

A__      :	Tuple          =    {
    """EleutherAI/gpt-neo-1.3B""": """https://huggingface.co/EleutherAI/gpt-neo-1.3B/resolve/main/config.json""",
    # See all GPTNeo models at https://huggingface.co/models?filter=gpt_neo
}







class   _lowercase						(       lowerCAmelCase_				):


     '''simple docstring'''





     _A								=							'gpt_neo'
     _A								=							['past_key_values']
     _A								=							{'num_attention_heads': 'num_heads', 'num_hidden_layers': 'num_layers'}



     def __init__(      self ,			__UpperCamelCase=5_02_57 ,			__UpperCamelCase=20_48 ,			__UpperCamelCase=20_48 ,			__UpperCamelCase=24 ,			__UpperCamelCase=[[["global", "local"], 12]] ,			__UpperCamelCase=16 ,			__UpperCamelCase=None ,			__UpperCamelCase=2_56 ,			__UpperCamelCase="gelu_new" ,			__UpperCamelCase=0.0 ,			__UpperCamelCase=0.0 ,			__UpperCamelCase=0.0 ,			__UpperCamelCase=0.1 ,			__UpperCamelCase=1E-5 ,			__UpperCamelCase=0.02 ,			__UpperCamelCase=True ,			__UpperCamelCase=5_02_56 ,			__UpperCamelCase=5_02_56 ,			**__UpperCamelCase ,			)->					List[Any]:
          UpperCAmelCase__							: List[str] 							=						vocab_size
          UpperCAmelCase__							: Optional[Any] 							=						max_position_embeddings
          UpperCAmelCase__							: Optional[Any] 							=						hidden_size
          UpperCAmelCase__							: Optional[int] 							=						num_layers
          UpperCAmelCase__							: Optional[Any] 							=						num_heads
          UpperCAmelCase__							: Any 							=						intermediate_size
          UpperCAmelCase__							: str 							=						window_size
          UpperCAmelCase__							: Union[str, Any] 							=						activation_function
          UpperCAmelCase__							: Optional[int] 							=						resid_dropout
          UpperCAmelCase__							: str 							=						embed_dropout
          UpperCAmelCase__							: str 							=						attention_dropout
          UpperCAmelCase__							: Optional[Any] 							=						classifier_dropout
          UpperCAmelCase__							: str 							=						layer_norm_epsilon
          UpperCAmelCase__							: Optional[int] 							=						initializer_range
          UpperCAmelCase__							: int 							=						use_cache

          UpperCAmelCase__							: Dict 							=						bos_token_id
          UpperCAmelCase__							: Tuple 							=						eos_token_id

          UpperCAmelCase__							: List[Any] 							=						attention_types
          UpperCAmelCase__							: Dict 							=						self.expand_attention_types_params(__UpperCamelCase  )

          if len(self.attention_layers  ) != self.num_layers:
               raise ValueError(
                   "Configuration for convolutional module is incorrect. "
                   "It is required that `len(config.attention_layers)` == `config.num_layers` "
                   F"but is `len(config.attention_layers) = {len(self.attention_layers  )}`, "
                   F"`config.num_layers = {self.num_layers}`. "
                   "`config.attention_layers` is prepared using `config.attention_types`. "
                   "Please verify the value of `config.attention_types` argument."  )

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



     @staticmethod
     def  lowerCAmelCase__       (      __UpperCamelCase  )->					Optional[Any]:
          UpperCAmelCase__							: List[str] 							=						[]
          for item in attention_types:
               for _ in range(item[1]  ):
                    attentions.extend(item[0]  )
          return attentions





def 							a__ (				lowerCAmelCase	:       Optional[Any]       ,    lowerCAmelCase	:       Dict       ,    lowerCAmelCase	:       Tuple       ,    lowerCAmelCase	:       str		):






     '''simple docstring'''
     import torch

     UpperCAmelCase__							: str 							=						input.size()
     UpperCAmelCase__							: List[Any] 							=						len(lowerCAmelCase		)
     UpperCAmelCase__							: List[Any] 							=						shape[dimension]

     UpperCAmelCase__							: Dict 							=						torch.arange(0       ,    lowerCAmelCase       ,    lowerCAmelCase		)
     UpperCAmelCase__							: List[Any] 							=						torch.div(sizedim - size       ,    lowerCAmelCase       ,    rounding_mode="floor"		) + 1
     UpperCAmelCase__							: int 							=						torch.arange(lowerCAmelCase		) + low_indices[:min_length][:, None]

     UpperCAmelCase__							: int 							=						[slice(lowerCAmelCase		)] * rank
     UpperCAmelCase__							: List[Any] 							=						indices
     UpperCAmelCase__							: List[Any] 							=						input[s]

     UpperCAmelCase__							: List[Any] 							=						list(range(0       ,    rank + 1		)		)
     perm.append(perm.pop(dimension + 1		)		)

     return sliced.permute(lowerCAmelCase		)



def 							a__ (				lowerCAmelCase	:       str       ,    lowerCAmelCase	:       Optional[Any]		):






     '''simple docstring'''
     import torch

     UpperCAmelCase__							: Any 							=						torch.arange(1       ,    lowerCAmelCase		)
     UpperCAmelCase__							: int 							=						torch.remainder(lowerCAmelCase       ,    lowerCAmelCase		)
     UpperCAmelCase__							: Any 							=						remainders == 0
     UpperCAmelCase__							: Any 							=						candidates[divisor_indices]
     UpperCAmelCase__							: Union[str, Any] 							=						torch.max(lowerCAmelCase		)
     return largest_divisor, torch.div(lowerCAmelCase       ,    lowerCAmelCase       ,    rounding_mode="floor"		)







class   _lowercase						(       lowerCAmelCase_				):


     '''simple docstring'''





     @property
     def  lowerCAmelCase__       (      self  )->					Mapping[str, Mapping[int, str]]:
          UpperCAmelCase__							: Union[str, Any] 							=						OrderedDict({"input_ids": {0: "batch", 1: "sequence"}}  )
          if self.use_past:
               self.fill_with_past_key_values_(__UpperCamelCase ,			direction="inputs"  )
               UpperCAmelCase__							: List[Any] 							=						{0: "batch", 1: "past_sequence + sequence"}
          else:
               UpperCAmelCase__							: int 							=						{0: "batch", 1: "sequence"}

          return common_inputs



     @property
     def  lowerCAmelCase__       (      self  )->					int:
          return self._config.num_heads



     def  lowerCAmelCase__       (      self ,			__UpperCamelCase ,			__UpperCamelCase = -1 ,			__UpperCamelCase = -1 ,			__UpperCamelCase = False ,			__UpperCamelCase = None ,			)->					Mapping[str, Any]:
          UpperCAmelCase__							: List[str] 							=						super(__UpperCamelCase ,			self  ).generate_dummy_inputs(
              __UpperCamelCase ,			batch_size=__UpperCamelCase ,			seq_length=__UpperCamelCase ,			is_pair=__UpperCamelCase ,			framework=__UpperCamelCase  )

          # We need to order the input in the way they appears in the forward()
          UpperCAmelCase__							: str 							=						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

                    UpperCAmelCase__							,	UpperCAmelCase__							: Tuple 							=						common_inputs["input_ids"].shape
                    # Not using the same length for past_key_values
                    UpperCAmelCase__							: Union[str, Any] 							=						seqlen + 2
                    UpperCAmelCase__							: str 							=						(
                        batch,
                        self.num_attention_heads,
                        past_key_values_length,
                        self._config.hidden_size // self.num_attention_heads,
                    )
                    UpperCAmelCase__							: Optional[int] 							=						[
                        (torch.zeros(__UpperCamelCase  ), torch.zeros(__UpperCamelCase  )) for _ in range(self.num_layers  )
                    ]

          UpperCAmelCase__							: int 							=						common_inputs["attention_mask"]
          if self.use_past:
               UpperCAmelCase__							: Any 							=						ordered_inputs["attention_mask"].dtype
               UpperCAmelCase__							: Any 							=						torch.cat(
                   [ordered_inputs["attention_mask"], torch.ones(__UpperCamelCase ,			__UpperCamelCase ,			dtype=__UpperCamelCase  )] ,			dim=1  )

          return ordered_inputs



     @property
     def  lowerCAmelCase__       (      self  )->					int:
          return 13





"""simple docstring"""




import math



def 							a__ (				lowerCAmelCase	:       int		):






     '''simple docstring'''

     if 1 < number < 4:
          # 2 and 3 are primes
          return True
     elif number < 2 or number % 2 == 0 or number % 3 == 0:
          # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
          return False

     # All primes number are in format of 6k +/- 1
     for i in range(5       ,    int(math.sqrt(lowerCAmelCase		) + 1		)       ,    6		):
          if number % i == 0 or number % (i + 2) == 0:
               return False
     return True



def 							a__ (				lowerCAmelCase	:       int = 1_0001		):






     '''simple docstring'''

     try:
          UpperCAmelCase__							: List[str] 							=						int(lowerCAmelCase		)
     except (TypeError, ValueError):
          raise TypeError("Parameter nth must be int or castable to int."		) from None
     if nth <= 0:
          raise ValueError("Parameter nth must be greater than or equal to one."		)
     UpperCAmelCase__							: list[int] 							=						[]
     UpperCAmelCase__							: str 							=						2
     while len(lowerCAmelCase		) < nth:
          if is_prime(lowerCAmelCase		):
               primes.append(lowerCAmelCase		)
               num += 1
          else:
               num += 1
     return primes[len(lowerCAmelCase		) - 1]


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



