

'''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      lowerCAmelCase_    ( snake_case_	:			Tuple      )   ->				Any:


     '''simple docstring'''




     UpperCAmelCase_	   =       torch.exp(snake_case_      )
     UpperCAmelCase_	   =       torch.sum(snake_case_ ,   dim=1      )  # sum of exp(x_i)
     UpperCAmelCase_	   =       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   :   List[str]       ,      __a   :   Tuple			):
         super().__init__()
         UpperCAmelCase_	   =       config.output_attentions
         UpperCAmelCase_	   =       config.output_hidden_states
         UpperCAmelCase_	   =       nn.ModuleList([BertLayer(__a			) for _ in range(config.num_hidden_layers			)]			)
         UpperCAmelCase_	   =       nn.ModuleList([BertHighway(__a			) for _ in range(config.num_hidden_layers			)]			)

         UpperCAmelCase_	   =       [-1 for _ in range(config.num_hidden_layers			)]



    def  _lowercase						(self   :   Any       ,      __a   :   Dict			):
         if (type(__a			) is float) or (type(__a			) is int):
              for i in range(len(self.early_exit_entropy			)			):
                   UpperCAmelCase_	   =       x
         else:
              UpperCAmelCase_	   =       x



    def  _lowercase						(self   :   str       ,      __a   :   Dict			):
         UpperCAmelCase_	   =       pooler.state_dict()
         for highway in self.highway:
              for name, param in highway.pooler.state_dict().items():
                   param.copy_(loaded_model[name]			)






    def  _lowercase						(self   :   Optional[Any]       ,      __a   :   Any       ,      __a   :   Optional[int]=None       ,      __a   :   int=None       ,      __a   :   Dict=None       ,      __a   :   Any=None       ,      ):
         UpperCAmelCase_	   =       ()
         UpperCAmelCase_	   =       ()
         UpperCAmelCase_	   =       ()
         for i, layer_module in enumerate(self.layer			):
              if self.output_hidden_states:
                   UpperCAmelCase_	   =       all_hidden_states + (hidden_states,)

              UpperCAmelCase_	   =       layer_module(
                  __a       ,      __a       ,      head_mask[i]       ,      __a       ,      __a			)
              UpperCAmelCase_	   =       layer_outputs[0]

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

              UpperCAmelCase_	   =       (hidden_states,)
              if self.output_hidden_states:
                   UpperCAmelCase_	   =       current_outputs + (all_hidden_states,)
              if self.output_attentions:
                   UpperCAmelCase_	   =       current_outputs + (all_attentions,)

              UpperCAmelCase_	   =       self.highway[i](__a			)
              # logits, pooled_output

              if not self.training:
                   UpperCAmelCase_	   =       highway_exit[0]
                   UpperCAmelCase_	   =       entropy(__a			)
                   UpperCAmelCase_	   =       highway_exit + (highway_entropy,)  # logits, hidden_states(?), entropy
                   UpperCAmelCase_	   =       all_highway_exits + (highway_exit,)

                   if highway_entropy < self.early_exit_entropy[i]:
                        UpperCAmelCase_	   =       (highway_logits,) + current_outputs[1:] + (all_highway_exits,)
                        raise HighwayException(__a       ,      i + 1			)
              else:
                   UpperCAmelCase_	   =       all_highway_exits + (highway_exit,)

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

         UpperCAmelCase_	   =       (hidden_states,)
         if self.output_hidden_states:
              UpperCAmelCase_	   =       outputs + (all_hidden_states,)
         if self.output_attentions:
              UpperCAmelCase_	   =       outputs + (all_attentions,)

         UpperCAmelCase_	   =       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). """		,     UpperCamelCase__		,     )
class 	__A				(			UpperCamelCase__     ):



    def __init__(self   :   List[str]       ,      __a   :   str			):
         super().__init__(__a			)
         UpperCAmelCase_	   =       config

         UpperCAmelCase_	   =       BertEmbeddings(__a			)
         UpperCAmelCase_	   =       DeeBertEncoder(__a			)
         UpperCAmelCase_	   =       BertPooler(__a			)

         self.init_weights()



    def  _lowercase						(self   :   Optional[int]			):
         self.encoder.init_highway_pooler(self.pooler			)



    def  _lowercase						(self   :   Optional[Any]			):
         return self.embeddings.word_embeddings



    def  _lowercase						(self   :   Union[str, Any]       ,      __a   :   Optional[Any]			):
         UpperCAmelCase_	   =       value



    def  _lowercase						(self   :   str       ,      __a   :   List[str]			):
         for layer, heads in heads_to_prune.items():
              self.encoder.layer[layer].attention.prune_heads(__a			)






    @add_start_docstrings_to_model_forward(__a			)
    def  _lowercase						(self   :   Dict       ,      __a   :   List[str]=None       ,      __a   :   Union[str, Any]=None       ,      __a   :   int=None       ,      __a   :   Optional[Any]=None       ,      __a   :   List[str]=None       ,      __a   :   Any=None       ,      __a   :   Optional[Any]=None       ,      __a   :   List[Any]=None       ,      ):
         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:
              UpperCAmelCase_	   =       input_ids.size()
         elif inputs_embeds is not None:
              UpperCAmelCase_	   =       inputs_embeds.size()[:-1]
         else:
              raise ValueError("You have to specify either input_ids or inputs_embeds"			)

         UpperCAmelCase_	   =       input_ids.device if input_ids is not None else inputs_embeds.device

         if attention_mask is None:
              UpperCAmelCase_	   =       torch.ones(__a       ,      device=__a			)
         if encoder_attention_mask is None:
              UpperCAmelCase_	   =       torch.ones(__a       ,      device=__a			)
         if token_type_ids is None:
              UpperCAmelCase_	   =       torch.zeros(__a       ,      dtype=torch.long       ,      device=__a			)

         # 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.
         UpperCAmelCase_	   =       self.get_extended_attention_mask(__a       ,      __a       ,      __a			)

         # 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:
              UpperCAmelCase_	   =       encoder_attention_mask[:, None, :, :]
         if encoder_attention_mask.dim() == 2:
              UpperCAmelCase_	   =       encoder_attention_mask[:, None, None, :]

         UpperCAmelCase_	   =       encoder_extended_attention_mask.to(
             dtype=next(self.parameters()			).dtype			)  # fp16 compatibility
         UpperCAmelCase_	   =       (1.0 - encoder_extended_attention_mask) * -10000.0

         # 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]
         UpperCAmelCase_	   =       self.get_head_mask(__a       ,      self.config.num_hidden_layers			)

         UpperCAmelCase_	   =       self.embeddings(
             input_ids=__a       ,      position_ids=__a       ,      token_type_ids=__a       ,      inputs_embeds=__a			)
         UpperCAmelCase_	   =       self.encoder(
             __a       ,      attention_mask=__a       ,      head_mask=__a       ,      encoder_hidden_states=__a       ,      encoder_attention_mask=__a       ,      )
         UpperCAmelCase_	   =       encoder_outputs[0]
         UpperCAmelCase_	   =       self.pooler(__a			)

         UpperCAmelCase_	   =       (
             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				(			UpperCamelCase__     ):



    def __init__(self   :   List[str]       ,      __a   :   Optional[Any]       ,      __a   :   Union[str, Any]			):
         UpperCAmelCase_	   =       message
         UpperCAmelCase_	   =       exit_layer  # start from 1!




class 	__A				(			nn.Module     ):



    def __init__(self   :   List[Any]       ,      __a   :   List[str]			):
         super().__init__()
         UpperCAmelCase_	   =       BertPooler(__a			)
         UpperCAmelCase_	   =       nn.Dropout(config.hidden_dropout_prob			)
         UpperCAmelCase_	   =       nn.Linear(config.hidden_size       ,      config.num_labels			)






    def  _lowercase						(self   :   Dict       ,      __a   :   Optional[Any]			):
         # Pooler
         UpperCAmelCase_	   =       encoder_outputs[0]
         UpperCAmelCase_	   =       self.pooler(__a			)
         # "return" pooler_output

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

         # Dropout and classification
         UpperCAmelCase_	   =       bmodel_output[1]

         UpperCAmelCase_	   =       self.dropout(__a			)
         UpperCAmelCase_	   =       self.classifier(__a			)

         return logits, pooled_output




@add_start_docstrings(
    """Bert Model (with early exiting - DeeBERT) with a classifier on top,
    also takes care of multi-layer training. """		,     UpperCamelCase__		,     )
class 	__A				(			UpperCamelCase__     ):



    def __init__(self   :   Any       ,      __a   :   Tuple			):
         super().__init__(__a			)
         UpperCAmelCase_	   =       config.num_labels
         UpperCAmelCase_	   =       config.num_hidden_layers

         UpperCAmelCase_	   =       DeeBertModel(__a			)
         UpperCAmelCase_	   =       nn.Dropout(config.hidden_dropout_prob			)
         UpperCAmelCase_	   =       nn.Linear(config.hidden_size       ,      self.config.num_labels			)

         self.init_weights()






    @add_start_docstrings_to_model_forward(__a			)
    def  _lowercase						(self   :   Union[str, Any]       ,      __a   :   str=None       ,      __a   :   Dict=None       ,      __a   :   List[Any]=None       ,      __a   :   List[str]=None       ,      __a   :   List[str]=None       ,      __a   :   List[str]=None       ,      __a   :   Optional[Any]=None       ,      __a   :   str=-1       ,      __a   :   Any=False       ,      ):
         UpperCAmelCase_	   =       self.num_layers
         try:
              UpperCAmelCase_	   =       self.bert(
                  __a       ,      attention_mask=__a       ,      token_type_ids=__a       ,      position_ids=__a       ,      head_mask=__a       ,      inputs_embeds=__a       ,      )
              # sequence_output, pooled_output, (hidden_states), (attentions), highway exits

              UpperCAmelCase_	   =       outputs[1]

              UpperCAmelCase_	   =       self.dropout(__a			)
              UpperCAmelCase_	   =       self.classifier(__a			)
              UpperCAmelCase_	   =       (logits,) + outputs[2:]  # add hidden states and attention if they are here
         except HighwayException as e:
              UpperCAmelCase_	   =       e.message
              UpperCAmelCase_	   =       e.exit_layer
              UpperCAmelCase_	   =       outputs[0]

         if not self.training:
              UpperCAmelCase_	   =       entropy(__a			)
              UpperCAmelCase_	   =       []
              UpperCAmelCase_	   =       []
         if labels is not None:
              if self.num_labels == 1:
                   #  We are doing regression
                   UpperCAmelCase_	   =       MSELoss()
                   UpperCAmelCase_	   =       loss_fct(logits.view(-1			)       ,      labels.view(-1			)			)
              else:
                   UpperCAmelCase_	   =       CrossEntropyLoss()
                   UpperCAmelCase_	   =       loss_fct(logits.view(-1       ,      self.num_labels			)       ,      labels.view(-1			)			)

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

              if train_highway:
                   UpperCAmelCase_	   =       (sum(highway_losses[:-1]			),) + outputs
                   # exclude the final highway, of course
              else:
                   UpperCAmelCase_	   =       (loss,) + outputs
         if not self.training:
              UpperCAmelCase_	   =       outputs + ((original_entropy, highway_entropy), exit_layer)
              if output_layer >= 0:
                   UpperCAmelCase_	   =       (
                       (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'''





def      lowerCAmelCase_    ( snake_case_	:			int = 1_00_00_00      )   ->				int:


     '''simple docstring'''




     UpperCAmelCase_	   =       limit + 1
     UpperCAmelCase_	   =       [0] * limit
     for first_term in range(1 ,   snake_case_      ):
          for n in range(snake_case_ ,   snake_case_ ,   snake_case_      ):
               UpperCAmelCase_	   =       first_term + n / first_term
               if common_difference % 4:  # d must be divisble by 4
                    continue
               else:
                    common_difference /= 4
                    if (
                        first_term > common_difference
                        and first_term < 4 * common_difference
                    ):  # since x,y,z are positive integers
                         frequency[n] += 1  # so z>0 and a>d ,also 4d<a

     UpperCAmelCase_	   =       sum(1 for x in frequency[1:limit] if x == 10      )

     return count


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




