

'''simple docstring'''
import torch
from torch import nn
from torch.nn import CrossEntropyLoss, MSELoss

from transformers.file_utils import add_start_docstrings, add_start_docstrings_to_model_forward
from transformers.models.bert.modeling_bert import (
    BERT_INPUTS_DOCSTRING,
    BERT_START_DOCSTRING,
    BertEmbeddings,
    BertLayer,
    BertPooler,
    BertPreTrainedModel,
)







def  _A		(     snake_case					)      ->     Optional[int]:
   _lowercase      :				int      					=       torch.exp(snake_case					)
   _lowercase      :				Optional[Any]      					=       torch.sum(snake_case		,							dim=1					)  # sum of exp(x_i)
   _lowercase      :				str      					=       torch.sum(x * exp_x		,							dim=1					)  # sum of x_i * exp(x_i)
   return torch.log(snake_case					) - B / A


class        a__  (							nn.Module  ):


   def __init__(			self      ,    _UpperCamelCase  ):





      """simple docstring"""





      super().__init__()
      _lowercase      :				Union[str, Any]      					=       config.output_attentions
      _lowercase      :				Any      					=       config.output_hidden_states
      _lowercase      :				Optional[int]      					=       nn.ModuleList([BertLayer(_UpperCamelCase  ) for _ in range(config.num_hidden_layers  )]  )
      _lowercase      :				List[Any]      					=       nn.ModuleList([BertHighway(_UpperCamelCase  ) for _ in range(config.num_hidden_layers  )]  )

      _lowercase      :				Any      					=       [-1 for _ in range(config.num_hidden_layers  )]


   def 						_lowerCamelCase       (			self      ,    _UpperCamelCase  ):





      """simple docstring"""





      if (type(_UpperCamelCase  ) is float) or (type(_UpperCamelCase  ) is int):
         for i in range(len(self.early_exit_entropy  )  ):
            _lowercase      :				int      					=       x
      else:
         _lowercase      :				Any      					=       x


   def 						_lowerCamelCase       (			self      ,    _UpperCamelCase  ):





      """simple docstring"""





      _lowercase      :				Tuple      					=       pooler.state_dict()
      for highway in self.highway:
         for name, param in highway.pooler.state_dict().items():
            param.copy_(loaded_model[name]  )






   def 						_lowerCamelCase       (			self      ,    _UpperCamelCase      ,    _UpperCamelCase=None      ,    _UpperCamelCase=None      ,    _UpperCamelCase=None      ,    _UpperCamelCase=None      ,    ):





      """simple docstring"""





      _lowercase      :				Tuple      					=       ()
      _lowercase      :				Any      					=       ()
      _lowercase      :				Union[str, Any]      					=       ()
      for i, layer_module in enumerate(self.layer  ):
         if self.output_hidden_states:
            _lowercase      :				Dict      					=       all_hidden_states + (hidden_states,)

         _lowercase      :				Any      					=       layer_module(
             _UpperCamelCase      ,    _UpperCamelCase      ,    head_mask[i]      ,    _UpperCamelCase      ,    _UpperCamelCase  )
         _lowercase      :				Optional[int]      					=       layer_outputs[0]

         if self.output_attentions:
            _lowercase      :				Tuple      					=       all_attentions + (layer_outputs[1],)

         _lowercase      :				Optional[Any]      					=       (hidden_states,)
         if self.output_hidden_states:
            _lowercase      :				Optional[Any]      					=       current_outputs + (all_hidden_states,)
         if self.output_attentions:
            _lowercase      :				Union[str, Any]      					=       current_outputs + (all_attentions,)

         _lowercase      :				List[Any]      					=       self.highway[i](_UpperCamelCase  )
         # logits, pooled_output

         if not self.training:
            _lowercase      :				Tuple      					=       highway_exit[0]
            _lowercase      :				List[Any]      					=       entropy(_UpperCamelCase  )
            _lowercase      :				Tuple      					=       highway_exit + (highway_entropy,)  # logits, hidden_states(?), entropy
            _lowercase      :				Dict      					=       all_highway_exits + (highway_exit,)

            if highway_entropy < self.early_exit_entropy[i]:
               _lowercase      :				List[str]      					=       (highway_logits,) + current_outputs[1:] + (all_highway_exits,)
               raise HighwayException(_UpperCamelCase      ,    i + 1  )
         else:
            _lowercase      :				Union[str, Any]      					=       all_highway_exits + (highway_exit,)

        # Add last layer
      if self.output_hidden_states:
         _lowercase      :				Dict      					=       all_hidden_states + (hidden_states,)

      _lowercase      :				Tuple      					=       (hidden_states,)
      if self.output_hidden_states:
         _lowercase      :				List[str]      					=       outputs + (all_hidden_states,)
      if self.output_attentions:
         _lowercase      :				Union[str, Any]      					=       outputs + (all_attentions,)

      _lowercase      :				Tuple      					=       outputs + (all_highway_exits,)
      return outputs  # last-layer hidden state, (all hidden states), (all attentions), all highway exits




@add_start_docstrings(
    'The Bert Model transformer with early exiting (DeeBERT). '  ,				lowerCamelCase_  ,				)
class        a__  (							lowerCamelCase_  ):


   def __init__(			self      ,    _UpperCamelCase  ):





      """simple docstring"""





      super().__init__(_UpperCamelCase  )
      _lowercase      :				Tuple      					=       config

      _lowercase      :				Union[str, Any]      					=       BertEmbeddings(_UpperCamelCase  )
      _lowercase      :				Tuple      					=       DeeBertEncoder(_UpperCamelCase  )
      _lowercase      :				Optional[Any]      					=       BertPooler(_UpperCamelCase  )

      self.init_weights()


   def 						_lowerCamelCase       (			self  ):





      """simple docstring"""





      self.encoder.init_highway_pooler(self.pooler  )


   def 						_lowerCamelCase       (			self  ):





      """simple docstring"""





      return self.embeddings.word_embeddings


   def 						_lowerCamelCase       (			self      ,    _UpperCamelCase  ):





      """simple docstring"""





      _lowercase      :				Union[str, Any]      					=       value


   def 						_lowerCamelCase       (			self      ,    _UpperCamelCase  ):





      """simple docstring"""





      for layer, heads in heads_to_prune.items():
         self.encoder.layer[layer].attention.prune_heads(_UpperCamelCase  )






   @add_start_docstrings_to_model_forward(_UpperCamelCase  )
   def 						_lowerCamelCase       (			self      ,    _UpperCamelCase=None      ,    _UpperCamelCase=None      ,    _UpperCamelCase=None      ,    _UpperCamelCase=None      ,    _UpperCamelCase=None      ,    _UpperCamelCase=None      ,    _UpperCamelCase=None      ,    _UpperCamelCase=None      ,    ):





      """simple docstring"""





      if input_ids is not None and inputs_embeds is not None:
         raise ValueError("You cannot specify both input_ids and inputs_embeds at the same time"  )
      elif input_ids is not None:
         _lowercase      :				Union[str, Any]      					=       input_ids.size()
      elif inputs_embeds is not None:
         _lowercase      :				Optional[Any]      					=       inputs_embeds.size()[:-1]
      else:
         raise ValueError("You have to specify either input_ids or inputs_embeds"  )

      _lowercase      :				List[Any]      					=       input_ids.device if input_ids is not None else inputs_embeds.device

      if attention_mask is None:
         _lowercase      :				List[Any]      					=       torch.ones(_UpperCamelCase      ,    device=_UpperCamelCase  )
      if encoder_attention_mask is None:
         _lowercase      :				Tuple      					=       torch.ones(_UpperCamelCase      ,    device=_UpperCamelCase  )
      if token_type_ids is None:
         _lowercase      :				Dict      					=       torch.zeros(_UpperCamelCase      ,    dtype=torch.long      ,    device=_UpperCamelCase  )

      # We can provide a self-attention mask of dimensions [batch_size, from_seq_length, to_seq_length]
      # ourselves in which case we just need to make it broadcastable to all heads.
      _lowercase      :				torch.Tensor      					=       self.get_extended_attention_mask(_UpperCamelCase      ,    _UpperCamelCase      ,    _UpperCamelCase  )

      # If a 2D ou 3D attention mask is provided for the cross-attention
      # we need to make broadcastable to [batch_size, num_heads, seq_length, seq_length]
      if encoder_attention_mask.dim() == 3:
         _lowercase      :				Any      					=       encoder_attention_mask[:, None, :, :]
      if encoder_attention_mask.dim() == 2:
         _lowercase      :				Union[str, Any]      					=       encoder_attention_mask[:, None, None, :]

      _lowercase      :				int      					=       encoder_extended_attention_mask.to(
          dtype=next(self.parameters()  ).dtype  )  # fp16 compatibility
      _lowercase      :				Optional[int]      					=       (1.0 - encoder_extended_attention_mask) * -1_0_0_0_0.0

      # Prepare head mask if needed
      # 1.0 in head_mask indicate we keep the head
      # attention_probs has shape bsz x n_heads x N x N
      # input head_mask has shape [num_heads] or [num_hidden_layers x num_heads]
      # and head_mask is converted to shape [num_hidden_layers x batch x num_heads x seq_length x seq_length]
      _lowercase      :				Tuple      					=       self.get_head_mask(_UpperCamelCase      ,    self.config.num_hidden_layers  )

      _lowercase      :				Dict      					=       self.embeddings(
          input_ids=_UpperCamelCase      ,    position_ids=_UpperCamelCase      ,    token_type_ids=_UpperCamelCase      ,    inputs_embeds=_UpperCamelCase  )
      _lowercase      :				Any      					=       self.encoder(
          _UpperCamelCase      ,    attention_mask=_UpperCamelCase      ,    head_mask=_UpperCamelCase      ,    encoder_hidden_states=_UpperCamelCase      ,    encoder_attention_mask=_UpperCamelCase      ,    )
      _lowercase      :				Any      					=       encoder_outputs[0]
      _lowercase      :				List[Any]      					=       self.pooler(_UpperCamelCase  )

      _lowercase      :				Optional[int]      					=       (
          sequence_output,
          pooled_output,
      ) + encoder_outputs[
          1:
      ]  # add hidden_states and attentions if they are here
      return outputs  # sequence_output, pooled_output, (hidden_states), (attentions), highway exits




class        a__  (							lowerCamelCase_  ):


   def __init__(			self      ,    _UpperCamelCase      ,    _UpperCamelCase  ):





      """simple docstring"""





      _lowercase      :				List[Any]      					=       message
      _lowercase      :				List[str]      					=       exit_layer  # start from 1!




class        a__  (							nn.Module  ):


   def __init__(			self      ,    _UpperCamelCase  ):





      """simple docstring"""





      super().__init__()
      _lowercase      :				Optional[int]      					=       BertPooler(_UpperCamelCase  )
      _lowercase      :				Tuple      					=       nn.Dropout(config.hidden_dropout_prob  )
      _lowercase      :				Optional[Any]      					=       nn.Linear(config.hidden_size      ,    config.num_labels  )






   def 						_lowerCamelCase       (			self      ,    _UpperCamelCase  ):





      """simple docstring"""





      _lowercase      :				Optional[Any]      					=       encoder_outputs[0]
      _lowercase      :				Optional[Any]      					=       self.pooler(_UpperCamelCase  )
      # "return" pooler_output

      # BertModel
      _lowercase      :				List[str]      					=       (pooler_input, pooler_output) + encoder_outputs[1:]
      # "return" bmodel_output

      # Dropout and classification
      _lowercase      :				Any      					=       bmodel_output[1]

      _lowercase      :				Optional[Any]      					=       self.dropout(_UpperCamelCase  )
      _lowercase      :				Optional[int]      					=       self.classifier(_UpperCamelCase  )

      return logits, pooled_output




@add_start_docstrings(
    'Bert Model (with early exiting - DeeBERT) with a classifier on top,\n    also takes care of multi-layer training. '  ,				lowerCamelCase_  ,				)
class        a__  (							lowerCamelCase_  ):


   def __init__(			self      ,    _UpperCamelCase  ):





      """simple docstring"""





      super().__init__(_UpperCamelCase  )
      _lowercase      :				Dict      					=       config.num_labels
      _lowercase      :				Any      					=       config.num_hidden_layers

      _lowercase      :				List[str]      					=       DeeBertModel(_UpperCamelCase  )
      _lowercase      :				Any      					=       nn.Dropout(config.hidden_dropout_prob  )
      _lowercase      :				Optional[Any]      					=       nn.Linear(config.hidden_size      ,    self.config.num_labels  )

      self.init_weights()






   @add_start_docstrings_to_model_forward(_UpperCamelCase  )
   def 						_lowerCamelCase       (			self      ,    _UpperCamelCase=None      ,    _UpperCamelCase=None      ,    _UpperCamelCase=None      ,    _UpperCamelCase=None      ,    _UpperCamelCase=None      ,    _UpperCamelCase=None      ,    _UpperCamelCase=None      ,    _UpperCamelCase=-1      ,    _UpperCamelCase=False      ,    ):





      """simple docstring"""





      _lowercase      :				Tuple      					=       self.num_layers
      try:
         _lowercase      :				Dict      					=       self.bert(
             _UpperCamelCase      ,    attention_mask=_UpperCamelCase      ,    token_type_ids=_UpperCamelCase      ,    position_ids=_UpperCamelCase      ,    head_mask=_UpperCamelCase      ,    inputs_embeds=_UpperCamelCase      ,    )
         # sequence_output, pooled_output, (hidden_states), (attentions), highway exits

         _lowercase      :				List[str]      					=       outputs[1]

         _lowercase      :				int      					=       self.dropout(_UpperCamelCase  )
         _lowercase      :				Any      					=       self.classifier(_UpperCamelCase  )
         _lowercase      :				Any      					=       (logits,) + outputs[2:]  # add hidden states and attention if they are here
      except HighwayException as e:
         _lowercase      :				Union[str, Any]      					=       e.message
         _lowercase      :				List[str]      					=       e.exit_layer
         _lowercase      :				List[Any]      					=       outputs[0]

      if not self.training:
         _lowercase      :				Optional[int]      					=       entropy(_UpperCamelCase  )
         _lowercase      :				Optional[int]      					=       []
         _lowercase      :				Dict      					=       []
      if labels is not None:
         if self.num_labels == 1:
            #  We are doing regression
            _lowercase      :				Optional[Any]      					=       MSELoss()
            _lowercase      :				List[Any]      					=       loss_fct(logits.view(-1  )      ,    labels.view(-1  )  )
         else:
            _lowercase      :				Tuple      					=       CrossEntropyLoss()
            _lowercase      :				Union[str, Any]      					=       loss_fct(logits.view(-1      ,    self.num_labels  )      ,    labels.view(-1  )  )

         # work with highway exits
         _lowercase      :				str      					=       []
         for highway_exit in outputs[-1]:
            _lowercase      :				Any      					=       highway_exit[0]
            if not self.training:
               highway_logits_all.append(_UpperCamelCase  )
               highway_entropy.append(highway_exit[2]  )
            if self.num_labels == 1:
               #  We are doing regression
               _lowercase      :				Dict      					=       MSELoss()
               _lowercase      :				List[str]      					=       loss_fct(highway_logits.view(-1  )      ,    labels.view(-1  )  )
            else:
               _lowercase      :				Dict      					=       CrossEntropyLoss()
               _lowercase      :				int      					=       loss_fct(highway_logits.view(-1      ,    self.num_labels  )      ,    labels.view(-1  )  )
            highway_losses.append(_UpperCamelCase  )

         if train_highway:
            _lowercase      :				int      					=       (sum(highway_losses[:-1]  ),) + outputs
            # exclude the final highway, of course
         else:
            _lowercase      :				int      					=       (loss,) + outputs
      if not self.training:
         _lowercase      :				List[str]      					=       outputs + ((original_entropy, highway_entropy), exit_layer)
         if output_layer >= 0:
            _lowercase      :				str      					=       (
                (outputs[0],) + (highway_logits_all[output_layer],) + outputs[2:]
            )  # use the highway of the last layer

      return outputs  # (loss), logits, (hidden_states), (attentions), (highway_exits)









'''simple docstring'''
from math import sqrt







def  _A		(     snake_case					)      ->     int:
   _lowercase      :				str      					=       0
   for i in range(1		,							int(sqrt(snake_case					) + 1					)					):
      if n % i == 0 and i != sqrt(snake_case					):
         total += i + n // i
      elif i == sqrt(snake_case					):
         total += i
   return total - n







def  _A		(     snake_case = 1_00_00					)      ->     int:
   _lowercase      :				List[Any]      					=       sum(
       i
       for i in range(1		,							snake_case					)
       if sum_of_divisors(sum_of_divisors(snake_case					)					) == i and sum_of_divisors(snake_case					) != i					)
   return total


if __name__ == "__main__":
    print(solution(int(str(input()).strip())))






