'''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 							UpperCamelCase__			(			a__      ):


						'''simple docstring'''






						_lowerCAmelCase										=torch.exp(a__      )
						_lowerCAmelCase										=torch.sum(a__			,      dim=1      )  # sum of exp(x_i)
						_lowerCAmelCase										=torch.sum(x * exp_x			,      dim=1      )  # sum of x_i * exp(x_i)
						return torch.log(a__      ) - B / A
class   SCREAMING_SNAKE_CASE			(						nn.Module):







		"""simple docstring"""






		def __init__(   self		,						__A				) ->     Optional[int]:
								super().__init__()
								_lowerCAmelCase										=config.output_attentions
								_lowerCAmelCase										=config.output_hidden_states
								_lowerCAmelCase										=nn.ModuleList([BertLayer(__A				) for _ in range(config.num_hidden_layers				)]				)
								_lowerCAmelCase										=nn.ModuleList([BertHighway(__A				) for _ in range(config.num_hidden_layers				)]				)

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






		def 		UpperCamelCase__       (   self		,						__A				) ->     Union[str, Any]:
								if (type(__A				) is float) or (type(__A				) is int):
														for i in range(len(self.early_exit_entropy				)				):
																				_lowerCAmelCase										=x
								else:
														_lowerCAmelCase										=x






		def 		UpperCamelCase__       (   self		,						__A				) ->     Union[str, Any]:
								_lowerCAmelCase										=pooler.state_dict()
								for highway in self.highway:
														for name, param in highway.pooler.state_dict().items():
																				param.copy_(loaded_model[name]				)






		def 		UpperCamelCase__       (   self		,						__A		,						__A=None		,						__A=None		,						__A=None		,						__A=None		,						) ->     Union[str, Any]:
								_lowerCAmelCase										=()
								_lowerCAmelCase										=()
								_lowerCAmelCase										=()
								for i, layer_module in enumerate(self.layer				):
														if self.output_hidden_states:
																				_lowerCAmelCase										=all_hidden_states + (hidden_states,)

														_lowerCAmelCase										=layer_module(
														    __A		,						__A		,						head_mask[i]		,						__A		,						__A				)
														_lowerCAmelCase										=layer_outputs[0]

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

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

														_lowerCAmelCase										=self.highway[i](__A				)
														# logits, pooled_output

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

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

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

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

								_lowerCAmelCase										=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). '    ,			__lowercase    ,			)
class   SCREAMING_SNAKE_CASE			(						__lowercase):







		"""simple docstring"""






		def __init__(   self		,						__A				) ->     Dict:
								super().__init__(__A				)
								_lowerCAmelCase										=config

								_lowerCAmelCase										=BertEmbeddings(__A				)
								_lowerCAmelCase										=DeeBertEncoder(__A				)
								_lowerCAmelCase										=BertPooler(__A				)

								self.init_weights()






		def 		UpperCamelCase__       (   self				) ->     Dict:
								self.encoder.init_highway_pooler(self.pooler				)






		def 		UpperCamelCase__       (   self				) ->     Any:
								return self.embeddings.word_embeddings






		def 		UpperCamelCase__       (   self		,						__A				) ->     Tuple:
								_lowerCAmelCase										=value






		def 		UpperCamelCase__       (   self		,						__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 		UpperCamelCase__       (   self		,						__A=None		,						__A=None		,						__A=None		,						__A=None		,						__A=None		,						__A=None		,						__A=None		,						__A=None		,						) ->     int:
								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:
														_lowerCAmelCase										=input_ids.size()
								elif inputs_embeds is not None:
														_lowerCAmelCase										=inputs_embeds.size()[:-1]
								else:
														raise ValueError('You have to specify either input_ids or inputs_embeds'				)

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

								if attention_mask is None:
														_lowerCAmelCase										=torch.ones(__A		,						device=__A				)
								if encoder_attention_mask is None:
														_lowerCAmelCase										=torch.ones(__A		,						device=__A				)
								if token_type_ids is None:
														_lowerCAmelCase										=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.
								_lowerCAmelCase										=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:
														_lowerCAmelCase										=encoder_attention_mask[:, None, :, :]
								if encoder_attention_mask.dim() == 2:
														_lowerCAmelCase										=encoder_attention_mask[:, None, None, :]

								_lowerCAmelCase										=encoder_extended_attention_mask.to(
								    dtype=next(self.parameters()				).dtype				)  # fp16 compatibility
								_lowerCAmelCase										=(1.0 - encoder_extended_attention_mask) * -10_000.0

								# 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]
								_lowerCAmelCase										=self.get_head_mask(__A		,						self.config.num_hidden_layers				)

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

								_lowerCAmelCase										=(
								    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   SCREAMING_SNAKE_CASE			(						__lowercase):







		"""simple docstring"""






		def __init__(   self		,						__A		,						__A				) ->     Dict:
								_lowerCAmelCase										=message
								_lowerCAmelCase										=exit_layer  # start from 1!

class   SCREAMING_SNAKE_CASE			(						nn.Module):







		"""simple docstring"""






		def __init__(   self		,						__A				) ->     int:
								super().__init__()
								_lowerCAmelCase										=BertPooler(__A				)
								_lowerCAmelCase										=nn.Dropout(config.hidden_dropout_prob				)
								_lowerCAmelCase										=nn.Linear(config.hidden_size		,						config.num_labels				)






		def 		UpperCamelCase__       (   self		,						__A				) ->     int:
								# Pooler
								_lowerCAmelCase										=encoder_outputs[0]
								_lowerCAmelCase										=self.pooler(__A				)
								# "return" pooler_output

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

								# Dropout and classification
								_lowerCAmelCase										=bmodel_output[1]

								_lowerCAmelCase										=self.dropout(__A				)
								_lowerCAmelCase										=self.classifier(__A				)

								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. '    ,			__lowercase    ,			)
class   SCREAMING_SNAKE_CASE			(						__lowercase):







		"""simple docstring"""






		def __init__(   self		,						__A				) ->     Union[str, Any]:
								super().__init__(__A				)
								_lowerCAmelCase										=config.num_labels
								_lowerCAmelCase										=config.num_hidden_layers

								_lowerCAmelCase										=DeeBertModel(__A				)
								_lowerCAmelCase										=nn.Dropout(config.hidden_dropout_prob				)
								_lowerCAmelCase										=nn.Linear(config.hidden_size		,						self.config.num_labels				)

								self.init_weights()






		@add_start_docstrings_to_model_forward(__A				)
		def 		UpperCamelCase__       (   self		,						__A=None		,						__A=None		,						__A=None		,						__A=None		,						__A=None		,						__A=None		,						__A=None		,						__A=-1		,						__A=False		,						) ->     Tuple:
								_lowerCAmelCase										=self.num_layers
								try:
														_lowerCAmelCase										=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

														_lowerCAmelCase										=outputs[1]

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

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

														# work with highway exits
														_lowerCAmelCase										=[]
														for highway_exit in outputs[-1]:
																				_lowerCAmelCase										=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
																										_lowerCAmelCase										=MSELoss()
																										_lowerCAmelCase										=loss_fct(highway_logits.view(-1				)		,						labels.view(-1				)				)
																				else:
																										_lowerCAmelCase										=CrossEntropyLoss()
																										_lowerCAmelCase										=loss_fct(highway_logits.view(-1		,						self.num_labels				)		,						labels.view(-1				)				)
																				highway_losses.append(__A				)

														if train_highway:
																				_lowerCAmelCase										=(sum(highway_losses[:-1]				),) + outputs
																				# exclude the final highway, of course
														else:
																				_lowerCAmelCase										=(loss,) + outputs
								if not self.training:
														_lowerCAmelCase										=outputs + ((original_entropy, highway_entropy), exit_layer)
														if output_layer >= 0:
																				_lowerCAmelCase										=(
																				    (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 							UpperCamelCase__			(			a__ = 1_0_0_0      ):


						'''simple docstring'''






						_lowerCAmelCase										=2**power
						_lowerCAmelCase										=0
						while n:
												_lowerCAmelCase						,				_lowerCAmelCase										=r + n % 1_0, n // 1_0
						return r


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





