





"""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


lowerCamelCase_          =	logging.get_logger(__name__)

lowerCamelCase_          =	{
    "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						):
							SCREAMING_SNAKE_CASE_     :   Any					=						'''gpt2'''
							SCREAMING_SNAKE_CASE_     :   Tuple					=						['''past_key_values''']
							SCREAMING_SNAKE_CASE_     :   Optional[int]					=						{
							    '''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__=5_02_57	,SCREAMING_SNAKE_CASE__=10_24	,SCREAMING_SNAKE_CASE__=7_68	,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__=0.0_2	,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__=5_02_56	,SCREAMING_SNAKE_CASE__=5_02_56	,SCREAMING_SNAKE_CASE__=False	,SCREAMING_SNAKE_CASE__=False	,**SCREAMING_SNAKE_CASE__	,)    ->   Dict:





													"""simple docstring"""






													__SCREAMING_SNAKE_CASE     :Optional[Any]	       =						vocab_size
													__SCREAMING_SNAKE_CASE     :Optional[int]	       =						n_positions
													__SCREAMING_SNAKE_CASE     :Tuple	       =						n_embd
													__SCREAMING_SNAKE_CASE     :Tuple	       =						n_layer
													__SCREAMING_SNAKE_CASE     :Union[str, Any]	       =						n_head
													__SCREAMING_SNAKE_CASE     :Tuple	       =						n_inner
													__SCREAMING_SNAKE_CASE     :int	       =						activation_function
													__SCREAMING_SNAKE_CASE     :List[Any]	       =						resid_pdrop
													__SCREAMING_SNAKE_CASE     :str	       =						embd_pdrop
													__SCREAMING_SNAKE_CASE     :Tuple	       =						attn_pdrop
													__SCREAMING_SNAKE_CASE     :Union[str, Any]	       =						layer_norm_epsilon
													__SCREAMING_SNAKE_CASE     :List[str]	       =						initializer_range
													__SCREAMING_SNAKE_CASE     :Optional[Any]	       =						summary_type
													__SCREAMING_SNAKE_CASE     :List[str]	       =						summary_use_proj
													__SCREAMING_SNAKE_CASE     :Any	       =						summary_activation
													__SCREAMING_SNAKE_CASE     :List[Any]	       =						summary_first_dropout
													__SCREAMING_SNAKE_CASE     :Optional[int]	       =						summary_proj_to_labels
													__SCREAMING_SNAKE_CASE     :Optional[int]	       =						scale_attn_weights
													__SCREAMING_SNAKE_CASE     :Dict	       =						use_cache
													__SCREAMING_SNAKE_CASE     :Union[str, Any]	       =						scale_attn_by_inverse_layer_idx
													__SCREAMING_SNAKE_CASE     :str	       =						reorder_and_upcast_attn

													__SCREAMING_SNAKE_CASE     :Optional[int]	       =						bos_token_id
													__SCREAMING_SNAKE_CASE     :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	,)    ->   Tuple:





													"""simple docstring"""






													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?
																			__SCREAMING_SNAKE_CASE     :int	       =						0




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





													"""simple docstring"""






													__SCREAMING_SNAKE_CASE     :Tuple	       =						OrderedDict({'''input_ids''': {0: '''batch''', 1: '''sequence'''}}							)
													if self.use_past:
																			self.fill_with_past_key_values_(SCREAMING_SNAKE_CASE__	,direction='''inputs'''							)
																			__SCREAMING_SNAKE_CASE     :Tuple	       =						{0: '''batch''', 1: '''past_sequence + sequence'''}
													else:
																			__SCREAMING_SNAKE_CASE     :int	       =						{0: '''batch''', 1: '''sequence'''}

													return common_inputs




							@property
							def 					_UpperCamelCase  (		self							)    ->   int:





													"""simple docstring"""






													return self._config.n_layer




							@property
							def 					_UpperCamelCase  (		self							)    ->   int:





													"""simple docstring"""






													return self._config.n_head




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





													"""simple docstring"""






													__SCREAMING_SNAKE_CASE     :Any	       =						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()
													__SCREAMING_SNAKE_CASE     :List[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

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

													__SCREAMING_SNAKE_CASE     :Any	       =						common_inputs['''attention_mask''']
													if self.use_past:
																			__SCREAMING_SNAKE_CASE     :int	       =						ordered_inputs['''attention_mask'''].dtype
																			__SCREAMING_SNAKE_CASE     :str	       =						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 					_UpperCamelCase  (		self							)    ->   int:





													"""simple docstring"""






													return 13






"""simple docstring"""
def   __lowerCamelCase     (							a_  :	int = 10**6							)    ->   int:

      if n <= 0:
            raise ValueError('''Please enter an integer greater than 0'''							)

      __SCREAMING_SNAKE_CASE     :Tuple	       =						list(range(n + 1							)							)
      for number in range(2				,     n + 1							):
            if phi[number] == number:
                  phi[number] -= 1
                  for multiple in range(number * 2				,     n + 1				,     a_							):
                        __SCREAMING_SNAKE_CASE     :List[Any]	       =						(phi[multiple] // number) * (number - 1)

      __SCREAMING_SNAKE_CASE     :Optional[Any]	       =						1
      for number in range(1				,     n + 1							):
            if (answer / phi[answer]) < (number / phi[number]):
                  __SCREAMING_SNAKE_CASE     :str	       =						number

      return answer


if __name__ == "__main__":
  print(solution())