






import torch
from torch import nn
from torch.nn import CrossEntropyLoss, MSELoss

from ....modeling_outputs import BaseModelOutputWithPooling, SequenceClassifierOutput
from ....modeling_utils import ModuleUtilsMixin
from ....utils import add_start_docstrings, add_start_docstrings_to_model_forward, logging, replace_return_docstrings


_a	 =     logging.get_logger(__name__)

_a	 =     '''MMBTConfig'''






class 							A_				(	nn.Module      ):


     def __init__(							self    :	Dict    ,						UpperCAmelCase    :	Dict    ,						UpperCAmelCase    :	Tuple    ,						UpperCAmelCase    :	Any      )							->			Dict:
      super().__init__()
      __lowerCAmelCase:     Optional[int]     			=   config
      __lowerCAmelCase:     Dict     			=   encoder
      __lowerCAmelCase:     Tuple     			=   nn.Linear(config.modal_hidden_size    ,						config.hidden_size      )
      __lowerCAmelCase:     Optional[Any]     			=   embeddings.position_embeddings
      __lowerCAmelCase:     Optional[Any]     			=   embeddings.token_type_embeddings
      __lowerCAmelCase:     Optional[Any]     			=   embeddings.word_embeddings
      __lowerCAmelCase:     Tuple     			=   embeddings.LayerNorm
      __lowerCAmelCase:     int     			=   nn.Dropout(p=config.hidden_dropout_prob      )


     def 						UpperCAmelCase						(							self    :	List[str]    ,						UpperCAmelCase    :	Union[str, Any]    ,						UpperCAmelCase    :	Any=None    ,						UpperCAmelCase    :	str=None    ,						UpperCAmelCase    :	List[Any]=None    ,						UpperCAmelCase    :	List[Any]=None      )							->			str:
      __lowerCAmelCase:     Any     			=   self.proj_embeddings(self.encoder(UpperCAmelCase      )      )
      __lowerCAmelCase:     Dict     			=   token_embeddings.size(1      )

      if start_token is not None:
       __lowerCAmelCase:     List[Any]     			=   self.word_embeddings(UpperCAmelCase      )
       seq_length += 1
       __lowerCAmelCase:     Optional[int]     			=   torch.cat([start_token_embeds.unsqueeze(1      ), token_embeddings]    ,						dim=1      )

      if end_token is not None:
       __lowerCAmelCase:     Dict     			=   self.word_embeddings(UpperCAmelCase      )
       seq_length += 1
       __lowerCAmelCase:     Optional[int]     			=   torch.cat([token_embeddings, end_token_embeds.unsqueeze(1      )]    ,						dim=1      )

      if position_ids is None:
       __lowerCAmelCase:     int     			=   torch.arange(UpperCAmelCase    ,						dtype=torch.long    ,						device=input_modal.device      )
       __lowerCAmelCase:     Dict     			=   position_ids.unsqueeze(0      ).expand(input_modal.size(0      )    ,						UpperCAmelCase      )

      if token_type_ids is None:
       __lowerCAmelCase:     Tuple     			=   torch.zeros(
           (input_modal.size(0      ), seq_length)    ,						dtype=torch.long    ,						device=input_modal.device      )

      __lowerCAmelCase:     int     			=   self.position_embeddings(UpperCAmelCase      )
      __lowerCAmelCase:     int     			=   self.token_type_embeddings(UpperCAmelCase      )
      __lowerCAmelCase:     Union[str, Any]     			=   token_embeddings + position_embeddings + token_type_embeddings
      __lowerCAmelCase:     Optional[Any]     			=   self.LayerNorm(UpperCAmelCase      )
      __lowerCAmelCase:     str     			=   self.dropout(UpperCAmelCase      )
      return embeddings







_a	 =     R'''
    MMBT model was proposed in [Supervised Multimodal Bitransformers for Classifying Images and
    Text](https://github.com/facebookresearch/mmbt) by Douwe Kiela, Suvrat Bhooshan, Hamed Firooz, Davide Testuggine.
    It\'s a supervised multimodal bitransformer model that fuses information from text and other image encoders, and
    obtain state-of-the-art performance on various multimodal classification benchmark tasks.

    This model inherits from [`PreTrainedModel`]. Check the superclass documentation for the generic methods the
    library implements for all its model (such as downloading or saving, resizing the input embeddings, pruning heads
    etc.)

    This model is also a PyTorch [torch.nn.Module](https://pytorch.org/docs/stable/nn.html#torch.nn.Module) subclass.
    Use it as a regular PyTorch Module and refer to the PyTorch documentation for all matter related to general usage
    and behavior.

    Parameters:
        config ([`MMBTConfig`]): Model configuration class with all the parameters of the model.
            Initializing with a config file does not load the weights associated with the model, only the
            configuration.
        transformer (`nn.Module`): A text transformer that is used by MMBT.
            It should have embeddings, encoder, and pooler attributes.
        encoder (`nn.Module`): Encoder for the second modality.
            It should take in a batch of modal inputs and return k, n dimension embeddings.
'''

_a	 =     R'''
    Args:
        input_modal (`torch.FloatTensor` of shape `(batch_size, ***)`):
            The other modality data. It will be the shape that the encoder for that type expects. e.g. With an Image
            Encoder, the shape would be (batch_size, channels, height, width)
        input_ids (`torch.LongTensor` of shape `(batch_size, sequence_length)`):
            Indices of input sequence tokens in the vocabulary. It does not expect [CLS] token to be added as it\'s
            appended to the end of other modality embeddings. Indices can be obtained using [`AutoTokenizer`]. See
            [`PreTrainedTokenizer.encode`] and [`PreTrainedTokenizer.__call__`] for details.

            [What are input IDs?](../glossary#input-ids)
        modal_start_tokens (`torch.LongTensor` of shape `(batch_size,)`, *optional*):
            Optional start token to be added to Other Modality Embedding. [CLS] Most commonly used for classification
            tasks.
        modal_end_tokens (`torch.LongTensor` of shape `(batch_size,)`, *optional*):
            Optional end token to be added to Other Modality Embedding. [SEP] Most commonly used.
        attention_mask (*optional*) `torch.FloatTensor` of shape `(batch_size, sequence_length)`:
            Mask to avoid performing attention on padding token indices. Mask values selected in `[0, 1]`:

            - 1 for tokens that are **not masked**,
            - 0 for tokens that are **masked**.

            [What are attention masks?](../glossary#attention-mask)
        token_type_ids (*optional*) `torch.LongTensor` of shape `(batch_size, sequence_length)`:
            Segment token indices to indicate first and second portions of the inputs. Indices are selected in `[0,
            1]`:

            - 0 corresponds to a *sentence A* token,
            - 1 corresponds to a *sentence B* token.

            [What are token type IDs?](../glossary#token-type-ids)
        modal_token_type_ids (*optional*) `torch.LongTensor` of shape `(batch_size, modal_sequence_length)`:
            Segment token indices to indicate different portions of the non-text modality. The embeddings from these
            tokens will be summed with the respective token embeddings for the non-text modality.
        position_ids (`torch.LongTensor` of shape `(batch_size, sequence_length)`, *optional*):
            Indices of positions of each input sequence tokens in the position embeddings. Selected in the range `[0,
            config.max_position_embeddings - 1]`.

            [What are position IDs?](../glossary#position-ids)
        modal_position_ids (`torch.LongTensor` of shape `(batch_size, modal_sequence_length)`, *optional*):
            Indices of positions of each input sequence tokens in the position embeddings for the non-text modality.
            Selected in the range `[0, config.max_position_embeddings - 1]`.

            [What are position IDs?](../glossary#position-ids)
        head_mask (`torch.FloatTensor` of shape `(num_heads,)` or `(num_layers, num_heads)`, *optional*):
            Mask to nullify selected heads of the self-attention modules. Mask values selected in `[0, 1]`:

            - 1 indicates the head is **not masked**,
            - 0 indicates the head is **masked**.

        inputs_embeds (`torch.FloatTensor` of shape `(batch_size, sequence_length, embedding_dim)`, *optional*):
            Optionally, instead of passing `input_ids` you can choose to directly pass an embedded representation. This
            is useful if you want more control over how to convert `input_ids` indices into associated vectors than the
            model\'s internal embedding lookup matrix.
        encoder_hidden_states (`torch.FloatTensor` of shape `(batch_size, sequence_length, hidden_size)`, *optional*):
            Sequence of hidden-states at the output of the last layer of the encoder. Used in the cross-attention if
            the model is configured as a decoder.
        encoder_attention_mask (`torch.FloatTensor` of shape `(batch_size, sequence_length)`, *optional*):
            Mask to avoid performing attention on the padding token indices of the encoder input. This mask is used in
            the cross-attention if the model is configured as a decoder. Mask values selected in `[0, 1]`:

            - 1 for tokens that are **not masked**,
            - 0 for tokens that are **masked**.

        output_attentions (`bool`, *optional*):
            Whether or not to return the attentions tensors of all attention layers. See `attentions` under returned
            tensors for more detail.
        output_hidden_states (`bool`, *optional*):
            Whether or not to return the hidden states of all layers. See `hidden_states` under returned tensors for
            more detail.
        return_dict (`bool`, *optional*):
            Whether or not to return a [`~utils.ModelOutput`] instead of a plain tuple.
'''






@add_start_docstrings(
    'The bare MMBT Model outputting raw hidden-states without any specific head on top.'							,			snake_case__							,			)
class 							A_				(	nn.Module							,			snake_case__      ):


     def __init__(							self    :	Union[str, Any]    ,						UpperCAmelCase    :	Any    ,						UpperCAmelCase    :	Union[str, Any]    ,						UpperCAmelCase    :	Any      )							->			Any:
      super().__init__()
      __lowerCAmelCase:     Optional[Any]     			=   config
      __lowerCAmelCase:     List[str]     			=   transformer
      __lowerCAmelCase:     Any     			=   ModalEmbeddings(UpperCAmelCase    ,						UpperCAmelCase    ,						transformer.embeddings      )


     @add_start_docstrings_to_model_forward(UpperCAmelCase      )
     @replace_return_docstrings(output_type=UpperCAmelCase    ,						config_class=_CONFIG_FOR_DOC      )
     def 						UpperCAmelCase						(							self    :	Dict    ,						UpperCAmelCase    :	List[Any]    ,						UpperCAmelCase    :	Dict=None    ,						UpperCAmelCase    :	Tuple=None    ,						UpperCAmelCase    :	Any=None    ,						UpperCAmelCase    :	str=None    ,						UpperCAmelCase    :	Dict=None    ,						UpperCAmelCase    :	Optional[int]=None    ,						UpperCAmelCase    :	List[Any]=None    ,						UpperCAmelCase    :	List[Any]=None    ,						UpperCAmelCase    :	int=None    ,						UpperCAmelCase    :	Optional[Any]=None    ,						UpperCAmelCase    :	Any=None    ,						UpperCAmelCase    :	Tuple=None    ,						UpperCAmelCase    :	Union[str, Any]=None    ,						UpperCAmelCase    :	Optional[int]=None    ,						UpperCAmelCase    :	Optional[Any]=None    ,						)							->			int:
      __lowerCAmelCase:     Optional[int]     			=   output_attentions if output_attentions is not None else self.config.output_attentions
      __lowerCAmelCase:     int     			=   (
          output_hidden_states if output_hidden_states is not None else self.config.output_hidden_states
      )
      __lowerCAmelCase:     str     			=   return_dict if return_dict is not None else self.config.use_return_dict

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

      __lowerCAmelCase:     Any     			=   input_ids.device if input_ids is not None else inputs_embeds.device

      __lowerCAmelCase:     Optional[int]     			=   self.modal_encoder(
          UpperCAmelCase    ,						start_token=UpperCAmelCase    ,						end_token=UpperCAmelCase    ,						position_ids=UpperCAmelCase    ,						token_type_ids=UpperCAmelCase    ,						)

      __lowerCAmelCase:     Union[str, Any]     			=   modal_embeddings.size()[:-1]

      if token_type_ids is None:
       __lowerCAmelCase:     Optional[int]     			=   torch.ones(UpperCAmelCase    ,						dtype=torch.long    ,						device=UpperCAmelCase      )

      __lowerCAmelCase:     str     			=   self.transformer.embeddings(
          input_ids=UpperCAmelCase    ,						position_ids=UpperCAmelCase    ,						token_type_ids=UpperCAmelCase    ,						inputs_embeds=UpperCAmelCase      )

      __lowerCAmelCase:     Optional[Any]     			=   torch.cat([modal_embeddings, txt_embeddings]    ,						1      )

      __lowerCAmelCase:     Tuple     			=   embedding_output.size()[:-1]

      if attention_mask is None:
       __lowerCAmelCase:     Optional[int]     			=   torch.ones(UpperCAmelCase    ,						device=UpperCAmelCase      )
      else:
       __lowerCAmelCase:     List[str]     			=   torch.cat(
           [torch.ones(UpperCAmelCase    ,						device=UpperCAmelCase    ,						dtype=torch.long      ), attention_mask]    ,						dim=1      )
      if encoder_attention_mask is None:
       __lowerCAmelCase:     Tuple     			=   torch.ones(UpperCAmelCase    ,						device=UpperCAmelCase      )
      else:
       __lowerCAmelCase:     Optional[int]     			=   torch.cat(
           [torch.ones(UpperCAmelCase    ,						device=UpperCAmelCase      ), encoder_attention_mask]    ,						dim=1      )

      __lowerCAmelCase:     Optional[int]     			=   self.get_extended_attention_mask(UpperCAmelCase    ,						UpperCAmelCase      )
      __lowerCAmelCase:     List[Any]     			=   self.invert_attention_mask(UpperCAmelCase      )
      __lowerCAmelCase:     str     			=   self.get_head_mask(UpperCAmelCase    ,						self.config.num_hidden_layers      )

      __lowerCAmelCase:     Union[str, Any]     			=   self.transformer.encoder(
          UpperCAmelCase    ,						attention_mask=UpperCAmelCase    ,						head_mask=UpperCAmelCase    ,						encoder_hidden_states=UpperCAmelCase    ,						encoder_attention_mask=UpperCAmelCase    ,						output_attentions=UpperCAmelCase    ,						output_hidden_states=UpperCAmelCase    ,						return_dict=UpperCAmelCase    ,						)

      __lowerCAmelCase:     Dict     			=   encoder_outputs[0]
      __lowerCAmelCase:     Union[str, Any]     			=   self.transformer.pooler(UpperCAmelCase      )

      if not return_dict:
       return (sequence_output, pooled_output) + encoder_outputs[1:]

      return BaseModelOutputWithPooling(
          last_hidden_state=UpperCAmelCase    ,						pooler_output=UpperCAmelCase    ,						hidden_states=encoder_outputs.hidden_states    ,						attentions=encoder_outputs.attentions    ,						)


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


     def 						UpperCAmelCase						(							self    :	Dict    ,						UpperCAmelCase    :	List[str]      )							->			str:
      __lowerCAmelCase:     Tuple     			=   value







@add_start_docstrings(
    '\n    MMBT Model with a sequence classification/regression head on top (a linear layer on top of the pooled output)\n    '							,			snake_case__							,			snake_case__							,			)
class 							A_				(	nn.Module      ):


     def __init__(							self    :	List[Any]    ,						UpperCAmelCase    :	Optional[Any]    ,						UpperCAmelCase    :	str    ,						UpperCAmelCase    :	Any      )							->			Optional[Any]:
      super().__init__()
      __lowerCAmelCase:     Tuple     			=   config.num_labels

      __lowerCAmelCase:     List[str]     			=   MMBTModel(UpperCAmelCase    ,						UpperCAmelCase    ,						UpperCAmelCase      )
      __lowerCAmelCase:     Tuple     			=   nn.Dropout(config.hidden_dropout_prob      )
      __lowerCAmelCase:     List[str]     			=   nn.Linear(config.hidden_size    ,						config.num_labels      )


     def 						UpperCAmelCase						(							self    :	int    ,						UpperCAmelCase    :	str    ,						UpperCAmelCase    :	Tuple=None    ,						UpperCAmelCase    :	Tuple=None    ,						UpperCAmelCase    :	str=None    ,						UpperCAmelCase    :	Optional[int]=None    ,						UpperCAmelCase    :	str=None    ,						UpperCAmelCase    :	Optional[Any]=None    ,						UpperCAmelCase    :	List[Any]=None    ,						UpperCAmelCase    :	Optional[Any]=None    ,						UpperCAmelCase    :	str=None    ,						UpperCAmelCase    :	Union[str, Any]=None    ,						UpperCAmelCase    :	Tuple=None    ,						UpperCAmelCase    :	Union[str, Any]=None    ,						)							->			Dict:
      __lowerCAmelCase:     Any     			=   return_dict if return_dict is not None else self.config.use_return_dict

      __lowerCAmelCase:     List[str]     			=   self.mmbt(
          input_modal=UpperCAmelCase    ,						input_ids=UpperCAmelCase    ,						modal_start_tokens=UpperCAmelCase    ,						modal_end_tokens=UpperCAmelCase    ,						attention_mask=UpperCAmelCase    ,						token_type_ids=UpperCAmelCase    ,						modal_token_type_ids=UpperCAmelCase    ,						position_ids=UpperCAmelCase    ,						modal_position_ids=UpperCAmelCase    ,						head_mask=UpperCAmelCase    ,						inputs_embeds=UpperCAmelCase    ,						return_dict=UpperCAmelCase    ,						)

      __lowerCAmelCase:     Dict     			=   outputs[1]

      __lowerCAmelCase:     Dict     			=   self.dropout(UpperCAmelCase      )
      __lowerCAmelCase:     Optional[int]     			=   self.classifier(UpperCAmelCase      )

      __lowerCAmelCase:     int     			=   None
      if labels is not None:
       if self.num_labels == 1:
        #  We are doing regression
        __lowerCAmelCase:     Tuple     			=   MSELoss()
        __lowerCAmelCase:     Optional[Any]     			=   loss_fct(logits.view(-1      )    ,						labels.view(-1      )      )
       else:
        __lowerCAmelCase:     Optional[Any]     			=   CrossEntropyLoss()
        __lowerCAmelCase:     Tuple     			=   loss_fct(logits.view(-1    ,						self.num_labels      )    ,						labels.view(-1      )      )

      if not return_dict:
       __lowerCAmelCase:     List[str]     			=   (logits,) + outputs[2:]
       return ((loss,) + output) if loss is not None else output

      return SequenceClassifierOutput(
          loss=UpperCAmelCase    ,						logits=UpperCAmelCase    ,						hidden_states=outputs.hidden_states    ,						attentions=outputs.attentions    ,						)








from math import floor, sqrt







def _a				( SCREAMING_SNAKE_CASE	:    int	)					->					int:

 """simple docstring"""






 __lowerCAmelCase:     Optional[int]     			=   0.0
 __lowerCAmelCase:     Any     			=   1.0
 __lowerCAmelCase:     List[str]     			=   int(sqrt(SCREAMING_SNAKE_CASE	)	)
 __lowerCAmelCase:     Union[str, Any]     			=   root
 __lowerCAmelCase:     List[str]     			=   0
 while integer_part != 2 * root:
  __lowerCAmelCase:     List[str]     			=   denominator * integer_part - numerator
  __lowerCAmelCase:     Optional[int]     			=   (n - numerator**2) / denominator
  __lowerCAmelCase:     Union[str, Any]     			=   int((root + numerator) / denominator	)
  period += 1
 return period







def _a				( SCREAMING_SNAKE_CASE	:    int = 1_00_00	)					->					int:

 """simple docstring"""






 __lowerCAmelCase:     Optional[int]     			=   0
 for i in range(2					,      n + 1	):
  __lowerCAmelCase:     List[str]     			=   sqrt(SCREAMING_SNAKE_CASE	)
  if sr - floor(SCREAMING_SNAKE_CASE	) != 0 and continuous_fraction_period(SCREAMING_SNAKE_CASE	) % 2 == 1:
   count_odd_periods += 1
 return count_odd_periods


if __name__ == "__main__":
  print(f"{solution(int(input().strip()))}")





