


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


__a   				=      logging.get_logger(__name__)

__a   				=      {
    '''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 				__SCREAMING_SNAKE_CASE   (			A__   ):
      A				:							str    							=     'gpt2'
      A				:							Optional[int]    							=     ['past_key_values']
      A				:							List[Any]    							=     {
          'hidden_size': 'n_embd',
          'max_position_embeddings': 'n_positions',
          'num_attention_heads': 'n_head',
          'num_hidden_layers': 'n_layer',
      }


      def __init__(							self							,						SCREAMING_SNAKE_CASE__=50257							,						SCREAMING_SNAKE_CASE__=1024							,						SCREAMING_SNAKE_CASE__=768							,						SCREAMING_SNAKE_CASE__=12							,						SCREAMING_SNAKE_CASE__=12							,						SCREAMING_SNAKE_CASE__=None							,						SCREAMING_SNAKE_CASE__="gelu_new"							,						SCREAMING_SNAKE_CASE__=0.1							,						SCREAMING_SNAKE_CASE__=0.1							,						SCREAMING_SNAKE_CASE__=0.1							,						SCREAMING_SNAKE_CASE__=1E-5							,						SCREAMING_SNAKE_CASE__=0.02							,						SCREAMING_SNAKE_CASE__="cls_index"							,						SCREAMING_SNAKE_CASE__=True							,						SCREAMING_SNAKE_CASE__=None							,						SCREAMING_SNAKE_CASE__=True							,						SCREAMING_SNAKE_CASE__=0.1							,						SCREAMING_SNAKE_CASE__=True							,						SCREAMING_SNAKE_CASE__=True							,						SCREAMING_SNAKE_CASE__=50256							,						SCREAMING_SNAKE_CASE__=50256							,						SCREAMING_SNAKE_CASE__=False							,						SCREAMING_SNAKE_CASE__=False							,						**SCREAMING_SNAKE_CASE__							,						):
            lowercase			:   Dict					   =		vocab_size
            lowercase			:   Union[str, Any]					   =		n_positions
            lowercase			:   Tuple					   =		n_embd
            lowercase			:   Union[str, Any]					   =		n_layer
            lowercase			:   Dict					   =		n_head
            lowercase			:   str					   =		n_inner
            lowercase			:   Union[str, Any]					   =		activation_function
            lowercase			:   List[str]					   =		resid_pdrop
            lowercase			:   Dict					   =		embd_pdrop
            lowercase			:   int					   =		attn_pdrop
            lowercase			:   Optional[Any]					   =		layer_norm_epsilon
            lowercase			:   int					   =		initializer_range
            lowercase			:   List[Any]					   =		summary_type
            lowercase			:   Dict					   =		summary_use_proj
            lowercase			:   Tuple					   =		summary_activation
            lowercase			:   Union[str, Any]					   =		summary_first_dropout
            lowercase			:   Union[str, Any]					   =		summary_proj_to_labels
            lowercase			:   List[str]					   =		scale_attn_weights
            lowercase			:   Optional[int]					   =		use_cache
            lowercase			:   Optional[int]					   =		scale_attn_by_inverse_layer_idx
            lowercase			:   Union[str, Any]					   =		reorder_and_upcast_attn

            lowercase			:   Union[str, Any]					   =		bos_token_id
            lowercase			:   Optional[int]					   =		eos_token_id

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







class 				__SCREAMING_SNAKE_CASE   (			A__   ):


      def __init__(							self							,						SCREAMING_SNAKE_CASE__							,						SCREAMING_SNAKE_CASE__ = "default"							,						SCREAMING_SNAKE_CASE__ = None							,						SCREAMING_SNAKE_CASE__ = False							,						):
            super().__init__(SCREAMING_SNAKE_CASE__							,						task=SCREAMING_SNAKE_CASE__							,						patching_specs=SCREAMING_SNAKE_CASE__							,						use_past=SCREAMING_SNAKE_CASE__		)
            if not getattr(self._config							,						'''pad_token_id'''							,						SCREAMING_SNAKE_CASE__		):
                  # TODO: how to do that better?
                  lowercase			:   Tuple					   =		0


      @property
      def        __lowerCamelCase			(							self		):
            lowercase			:   int					   =		OrderedDict({'''input_ids''': {0: '''batch''', 1: '''sequence'''}}		)
            if self.use_past:
                  self.fill_with_past_key_values_(SCREAMING_SNAKE_CASE__							,						direction='''inputs'''		)
                  lowercase			:   List[Any]					   =		{0: '''batch''', 1: '''past_sequence + sequence'''}
            else:
                  lowercase			:   Any					   =		{0: '''batch''', 1: '''sequence'''}

            return common_inputs


      @property
      def        __lowerCamelCase			(							self		):
            return self._config.n_layer


      @property
      def        __lowerCamelCase			(							self		):
            return self._config.n_head


      def        __lowerCamelCase			(							self							,						SCREAMING_SNAKE_CASE__							,						SCREAMING_SNAKE_CASE__ = -1							,						SCREAMING_SNAKE_CASE__ = -1							,						SCREAMING_SNAKE_CASE__ = False							,						SCREAMING_SNAKE_CASE__ = None							,						):
            lowercase			:   List[str]					   =		super(SCREAMING_SNAKE_CASE__							,						self		).generate_dummy_inputs(
                SCREAMING_SNAKE_CASE__							,						batch_size=SCREAMING_SNAKE_CASE__							,						seq_length=SCREAMING_SNAKE_CASE__							,						is_pair=SCREAMING_SNAKE_CASE__							,						framework=SCREAMING_SNAKE_CASE__		)

            # We need to order the input in the way they appears in the forward()
            lowercase			:   Union[str, Any]					   =		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

                        lowercase   ,			lowercase			:   List[Any]					   =		common_inputs['''input_ids'''].shape
                        # Not using the same length for past_key_values
                        lowercase			:   int					   =		seqlen + 2
                        lowercase			:   int					   =		(
                            batch,
                            self.num_attention_heads,
                            past_key_values_length,
                            self._config.hidden_size // self.num_attention_heads,
                        )
                        lowercase			:   Any					   =		[
                            (torch.zeros(SCREAMING_SNAKE_CASE__		), torch.zeros(SCREAMING_SNAKE_CASE__		)) for _ in range(self.num_layers		)
                        ]

            lowercase			:   str					   =		common_inputs['''attention_mask''']
            if self.use_past:
                  lowercase			:   Dict					   =		ordered_inputs['''attention_mask'''].dtype
                  lowercase			:   Tuple					   =		torch.cat(
                      [ordered_inputs['''attention_mask'''], torch.ones(SCREAMING_SNAKE_CASE__							,						SCREAMING_SNAKE_CASE__							,						dtype=SCREAMING_SNAKE_CASE__		)]							,						dim=1		)

            return ordered_inputs






      @property
      def        __lowerCamelCase			(							self		):
            return 13





import math




def 			__lowercase	(						_UpperCamelCase     )    ->Union[str, Any]:







      """simple docstring"""

      lowercase			:   List[Any]					   =		0
      if n % 2 == 0:
            count += 1
            while n % 2 == 0:
                  lowercase			:   Any					   =		int(n / 2     )
    # the n input value must be odd so that
    # we can skip one element (ie i += 2)

      lowercase			:   Optional[int]					   =		3

      while i <= int(math.sqrt(_UpperCamelCase     )     ):
            if n % i == 0:
                  count += 1
                  while n % i == 0:
                        lowercase			:   Optional[Any]					   =		int(n / i     )
            lowercase			:   str					   =		i + 2

      # this condition checks the prime
      # number n is greater than 2

      if n > 2:
            count += 1
      return count


if __name__ == "__main__":
  __a   				=      51_24_21_83
  print(F'''The number of distinct prime factors is/are {exact_prime_factor_count(n)}''')
  print(F'''The value of log(log(n)) is {math.log(math.log(n)):.4f}''')

