


def  __lowerCAmelCase					(SCREAMING_SNAKE_CASE = 100_0000      )->						List[Any]:




						"""simple docstring"""

						snake_case_ =   set(range(3      ,      lowerCamelCase_      ,      2      )      )
						primes.add(2      )
						for p in range(3      ,      lowerCamelCase_      ,      2      ):
												if p not in primes:
																		continue
												primes.difference_update(set(range(p * p      ,      lowerCamelCase_      ,      lowerCamelCase_      )      )      )

						snake_case_ =   [float(lowerCamelCase_      ) for n in range(limit + 1      )]

						for p in primes:
												for n in range(lowerCamelCase_      ,      limit + 1      ,      lowerCamelCase_      ):
																		phi[n] *= 1 - 1 / p

						return int(sum(phi[2:]      )      )


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



from dataclasses import dataclass
from typing import Optional, Tuple

import torch
from torch import nn
from transformers import RobertaPreTrainedModel, XLMRobertaConfig, XLMRobertaModel
from transformers.utils import ModelOutput







@dataclass
class lowerCAmelCase_		(				lowerCamelCase__ ):

 '''simple docstring'''

 __snake_case				=						None
 __snake_case				=						None
 __snake_case				=						None
 __snake_case				=						None







class lowerCAmelCase_		(				lowerCamelCase__ ):

 '''simple docstring'''

 def __init__(			self	,   _UpperCAmelCase=1	,   _UpperCAmelCase=0	,   _UpperCAmelCase=2	,   _UpperCAmelCase=5_12	,   _UpperCAmelCase="cls"	,   _UpperCAmelCase=False	,   _UpperCAmelCase=True	,   **_UpperCAmelCase	,   ):
       super().__init__(pad_token_id=_UpperCAmelCase	,   bos_token_id=_UpperCAmelCase	,   eos_token_id=_UpperCAmelCase	,   **_UpperCAmelCase      )
       snake_case_ =   project_dim
       snake_case_ =   pooler_fn
       snake_case_ =   learn_encoder
       snake_case_ =   use_attention_mask







class lowerCAmelCase_		(				lowerCamelCase__ ):

 '''simple docstring'''

 __snake_case				=						[R"pooler", R"logit_scale"]
 __snake_case				=						[R"position_ids", R"predictions.decoder.bias"]
 __snake_case				=						"roberta"
 __snake_case				=						RobertaSeriesConfig



 def __init__(			self	,   _UpperCAmelCase      ):
       super().__init__(_UpperCAmelCase      )
       snake_case_ =   XLMRobertaModel(_UpperCAmelCase      )
       snake_case_ =   nn.Linear(config.hidden_size	,   config.project_dim      )
       snake_case_ =   getattr(_UpperCAmelCase	,   '''has_pre_transformation'''	,   _UpperCAmelCase      )
       if self.has_pre_transformation:
             snake_case_ =   nn.Linear(config.hidden_size	,   config.project_dim      )
             snake_case_ =   nn.LayerNorm(config.hidden_size	,   eps=config.layer_norm_eps      )
       self.post_init()





 def 		UpperCamelCase__  (			self	,   _UpperCAmelCase = None	,   _UpperCAmelCase = None	,   _UpperCAmelCase = None	,   _UpperCAmelCase = None	,   _UpperCAmelCase = None	,   _UpperCAmelCase = None	,   _UpperCAmelCase = None	,   _UpperCAmelCase = None	,   _UpperCAmelCase = None	,   _UpperCAmelCase = None	,   _UpperCAmelCase = None	,   ):
       snake_case_ =   return_dict if return_dict is not None else self.config.use_return_dict

       snake_case_ =   self.base_model(
           input_ids=_UpperCAmelCase	,   attention_mask=_UpperCAmelCase	,   token_type_ids=_UpperCAmelCase	,   position_ids=_UpperCAmelCase	,   head_mask=_UpperCAmelCase	,   inputs_embeds=_UpperCAmelCase	,   encoder_hidden_states=_UpperCAmelCase	,   encoder_attention_mask=_UpperCAmelCase	,   output_attentions=_UpperCAmelCase	,   output_hidden_states=True if self.has_pre_transformation else output_hidden_states	,   return_dict=_UpperCAmelCase	,   )

       if self.has_pre_transformation:
             snake_case_ =   outputs['''hidden_states'''][-2]
             snake_case_ =   self.pre_LN(_UpperCAmelCase      )
             snake_case_ =   self.transformation_pre(_UpperCAmelCase      )

             return TransformationModelOutput(
                 projection_state=_UpperCAmelCase	,   last_hidden_state=outputs.last_hidden_state	,   hidden_states=outputs.hidden_states	,   attentions=outputs.attentions	,   )
       else:
             snake_case_ =   self.transformation(outputs.last_hidden_state      )
             return TransformationModelOutput(
                 projection_state=_UpperCAmelCase	,   last_hidden_state=outputs.last_hidden_state	,   hidden_states=outputs.hidden_states	,   attentions=outputs.attentions	,   )