





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    __lowercase   (      _SCREAMING_SNAKE_CASE	) ->   List[str]:


      '''simple docstring'''


      SCREAMING_SNAKE_CASE		=						torch.exp(A_	)
      SCREAMING_SNAKE_CASE		=						torch.sum(A_ ,						dim=1	)  # sum of exp(x_i)
      SCREAMING_SNAKE_CASE		=						torch.sum(x * exp_x ,						dim=1	)  # sum of x_i * exp(x_i)
      return torch.log(A_	) - B / A

class 		UpperCamelCase__ (      nn.Module   ):



     '''simple docstring'''

     def __init__(							self						:    str						,lowerCamelCase__						:    Optional[int]       )     ->		List[str]:




           '''simple docstring'''


           super().__init__()
           SCREAMING_SNAKE_CASE		=						config.output_attentions
           SCREAMING_SNAKE_CASE		=						config.output_hidden_states
           SCREAMING_SNAKE_CASE		=						nn.ModuleList([BertLayer(lowercase_       ) for _ in range(config.num_hidden_layers       )]       )
           SCREAMING_SNAKE_CASE		=						nn.ModuleList([BertHighway(lowercase_       ) for _ in range(config.num_hidden_layers       )]       )

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






     def 				SCREAMING_SNAKE_CASE__  (							self						:    List[str]						,lowerCamelCase__						:    List[Any]       )     ->		List[Any]:




           '''simple docstring'''


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






     def 				SCREAMING_SNAKE_CASE__  (							self						:    Any						,lowerCamelCase__						:    int       )     ->		Optional[int]:




           '''simple docstring'''


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






     def 				SCREAMING_SNAKE_CASE__  (							self						:    str						,lowerCamelCase__						:    Optional[int]						,lowerCamelCase__						:    Union[str, Any]=None						,lowerCamelCase__						:    Any=None						,lowerCamelCase__						:    Union[str, Any]=None						,lowerCamelCase__						:    Optional[Any]=None						,)     ->		Optional[Any]:




           '''simple docstring'''


           SCREAMING_SNAKE_CASE		=						()
           SCREAMING_SNAKE_CASE		=						()
           SCREAMING_SNAKE_CASE		=						()
           for i, layer_module in enumerate(self.layer       ):
                 if self.output_hidden_states:
                       SCREAMING_SNAKE_CASE		=						all_hidden_states + (hidden_states,)

                 SCREAMING_SNAKE_CASE		=						layer_module(
                     lowercase_						,lowercase_						,head_mask[i]						,lowercase_						,lowercase_       )
                 SCREAMING_SNAKE_CASE		=						layer_outputs[0]

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

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

                 SCREAMING_SNAKE_CASE		=						self.highway[i](lowercase_       )
                 # logits, pooled_output

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

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

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

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

           SCREAMING_SNAKE_CASE		=						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). "							,      a_							,      )
class 		UpperCamelCase__ (      a_   ):



     '''simple docstring'''

     def __init__(							self						:    List[str]						,lowerCamelCase__						:    Tuple       )     ->		List[str]:




           '''simple docstring'''


           super().__init__(lowercase_       )
           SCREAMING_SNAKE_CASE		=						config

           SCREAMING_SNAKE_CASE		=						BertEmbeddings(lowercase_       )
           SCREAMING_SNAKE_CASE		=						DeeBertEncoder(lowercase_       )
           SCREAMING_SNAKE_CASE		=						BertPooler(lowercase_       )

           self.init_weights()






     def 				SCREAMING_SNAKE_CASE__  (							self						:    str       )     ->		List[str]:




           '''simple docstring'''


           self.encoder.init_highway_pooler(self.pooler       )






     def 				SCREAMING_SNAKE_CASE__  (							self						:    Tuple       )     ->		List[str]:




           '''simple docstring'''


           return self.embeddings.word_embeddings






     def 				SCREAMING_SNAKE_CASE__  (							self						:    List[str]						,lowerCamelCase__						:    Optional[Any]       )     ->		Any:




           '''simple docstring'''


           SCREAMING_SNAKE_CASE		=						value






     def 				SCREAMING_SNAKE_CASE__  (							self						:    str						,lowerCamelCase__						:    Tuple       )     ->		Dict:




           '''simple docstring'''


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






     @add_start_docstrings_to_model_forward(lowercase_       )
     def 				SCREAMING_SNAKE_CASE__  (							self						:    Tuple						,lowerCamelCase__						:    int=None						,lowerCamelCase__						:    int=None						,lowerCamelCase__						:    Tuple=None						,lowerCamelCase__						:    Dict=None						,lowerCamelCase__						:    Dict=None						,lowerCamelCase__						:    Optional[int]=None						,lowerCamelCase__						:    Optional[int]=None						,lowerCamelCase__						:    str=None						,)     ->		Any:




           '''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:
                 SCREAMING_SNAKE_CASE		=						input_ids.size()
           elif inputs_embeds is not None:
                 SCREAMING_SNAKE_CASE		=						inputs_embeds.size()[:-1]
           else:
                 raise ValueError("""You have to specify either input_ids or inputs_embeds"""       )

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

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

           # 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.
           SCREAMING_SNAKE_CASE		=						self.get_extended_attention_mask(lowercase_						,lowercase_						,lowercase_       )

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

           SCREAMING_SNAKE_CASE		=						encoder_extended_attention_mask.to(
               dtype=next(self.parameters()       ).dtype       )  # fp16 compatibility
           SCREAMING_SNAKE_CASE		=						(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]
           SCREAMING_SNAKE_CASE		=						self.get_head_mask(lowercase_						,self.config.num_hidden_layers       )

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

           SCREAMING_SNAKE_CASE		=						(
               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 		UpperCamelCase__ (      a_   ):



     '''simple docstring'''

     def __init__(							self						:    Tuple						,lowerCamelCase__						:    Any						,lowerCamelCase__						:    int       )     ->		List[str]:




           '''simple docstring'''


           SCREAMING_SNAKE_CASE		=						message
           SCREAMING_SNAKE_CASE		=						exit_layer  # start from 1!

class 		UpperCamelCase__ (      nn.Module   ):



     '''simple docstring'''

     def __init__(							self						:    Optional[Any]						,lowerCamelCase__						:    Any       )     ->		Union[str, Any]:




           '''simple docstring'''


           super().__init__()
           SCREAMING_SNAKE_CASE		=						BertPooler(lowercase_       )
           SCREAMING_SNAKE_CASE		=						nn.Dropout(config.hidden_dropout_prob       )
           SCREAMING_SNAKE_CASE		=						nn.Linear(config.hidden_size						,config.num_labels       )






     def 				SCREAMING_SNAKE_CASE__  (							self						:    Tuple						,lowerCamelCase__						:    int       )     ->		Optional[Any]:




           '''simple docstring'''


           SCREAMING_SNAKE_CASE		=						encoder_outputs[0]
           SCREAMING_SNAKE_CASE		=						self.pooler(lowercase_       )
           # "return" pooler_output

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

           # Dropout and classification
           SCREAMING_SNAKE_CASE		=						bmodel_output[1]

           SCREAMING_SNAKE_CASE		=						self.dropout(lowercase_       )
           SCREAMING_SNAKE_CASE		=						self.classifier(lowercase_       )

           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. "							,      a_							,      )
class 		UpperCamelCase__ (      a_   ):



     '''simple docstring'''

     def __init__(							self						:    Optional[Any]						,lowerCamelCase__						:    str       )     ->		Union[str, Any]:




           '''simple docstring'''


           super().__init__(lowercase_       )
           SCREAMING_SNAKE_CASE		=						config.num_labels
           SCREAMING_SNAKE_CASE		=						config.num_hidden_layers

           SCREAMING_SNAKE_CASE		=						DeeBertModel(lowercase_       )
           SCREAMING_SNAKE_CASE		=						nn.Dropout(config.hidden_dropout_prob       )
           SCREAMING_SNAKE_CASE		=						nn.Linear(config.hidden_size						,self.config.num_labels       )

           self.init_weights()






     @add_start_docstrings_to_model_forward(lowercase_       )
     def 				SCREAMING_SNAKE_CASE__  (							self						:    Any						,lowerCamelCase__						:    Tuple=None						,lowerCamelCase__						:    Optional[int]=None						,lowerCamelCase__						:    List[Any]=None						,lowerCamelCase__						:    int=None						,lowerCamelCase__						:    Tuple=None						,lowerCamelCase__						:    Optional[Any]=None						,lowerCamelCase__						:    Optional[int]=None						,lowerCamelCase__						:    Dict=-1						,lowerCamelCase__						:    Dict=False						,)     ->		str:




           '''simple docstring'''


           SCREAMING_SNAKE_CASE		=						self.num_layers
           try:
                 SCREAMING_SNAKE_CASE		=						self.bert(
                     lowercase_						,attention_mask=lowercase_						,token_type_ids=lowercase_						,position_ids=lowercase_						,head_mask=lowercase_						,inputs_embeds=lowercase_						,)
                 # sequence_output, pooled_output, (hidden_states), (attentions), highway exits

                 SCREAMING_SNAKE_CASE		=						outputs[1]

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

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

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

                 if train_highway:
                       SCREAMING_SNAKE_CASE		=						(sum(highway_losses[:-1]       ),) + outputs
                       # exclude the final highway, of course
                 else:
                       SCREAMING_SNAKE_CASE		=						(loss,) + outputs
           if not self.training:
                 SCREAMING_SNAKE_CASE		=						outputs + ((original_entropy, highway_entropy), exit_layer)
                 if output_layer >= 0:
                       SCREAMING_SNAKE_CASE		=						(
                           (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 collections import defaultdict
from math import ceil, sqrt

def   __SCREAMING_SNAKE_CASE  (      A_ = 1_00_00_00						,     A_ = 10 ):
	lowerCAmelCase__	:						defaultdict  				=	defaultdict(A_ )

	for outer_width in range(3						,     (t_limit // 4) + 2 ):
		if outer_width * outer_width > t_limit:
			lowerCAmelCase__	:						int  				=	max(
			    ceil(sqrt(outer_width * outer_width - t_limit ) )						,     1 )
		else:
			lowerCAmelCase__	:						Tuple  				=	1

		hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

		for hole_width in range(A_						,     outer_width - 1						,     2 ):
			count[outer_width * outer_width - hole_width * hole_width] += 1

	return sum(1 for n in count.values() if 1 <= n <= 10 )


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




