

import inspect
import unittest

from transformers import DPTConfig
from transformers.file_utils import is_torch_available, is_vision_available
from transformers.models.auto import get_values
from transformers.testing_utils import require_torch, require_vision, slow, torch_device

from ...test_configuration_common import ConfigTester
from ...test_modeling_common import ModelTesterMixin, _config_zero_init, floats_tensor, ids_tensor
from ...test_pipeline_mixin import PipelineTesterMixin


if is_torch_available():
   import torch
   from torch import nn

   from transformers import MODEL_MAPPING, DPTForDepthEstimation, DPTForSemanticSegmentation, DPTModel
   from transformers.models.dpt.modeling_dpt import DPT_PRETRAINED_MODEL_ARCHIVE_LIST


if is_vision_available():
   from PIL import Image

   from transformers import DPTImageProcessor



class        _UpperCAmelCase :
  '''simple docstring'''







  def __init__( self	: List[Any]		,						UpperCamelCase__	: List[str]		,						UpperCamelCase__	: Any=2		,						UpperCamelCase__	: Tuple=32		,						UpperCamelCase__	: str=16		,						UpperCamelCase__	: List[str]=3		,						UpperCamelCase__	: Dict=True		,						UpperCamelCase__	: Optional[int]=True		,						UpperCamelCase__	: Optional[Any]=32		,						UpperCamelCase__	: int=4		,						UpperCamelCase__	: Union[str, Any]=[0, 1, 2, 3]		,						UpperCamelCase__	: Tuple=4		,						UpperCamelCase__	: Any=37		,						UpperCamelCase__	: Union[str, Any]="gelu"		,						UpperCamelCase__	: str=0.1		,						UpperCamelCase__	: Any=0.1		,						UpperCamelCase__	: Tuple=0.02		,						UpperCamelCase__	: Dict=3		,						UpperCamelCase__	: Union[str, Any]=False		,						UpperCamelCase__	: Union[str, Any]=None		,						):
        A    =				parent
        A    =				batch_size
        A    =				image_size
        A    =				patch_size
        A    =				num_channels
        A    =				is_training
        A    =				use_labels
        A    =				hidden_size
        A    =				num_hidden_layers
        A    =				backbone_out_indices
        A    =				num_attention_heads
        A    =				intermediate_size
        A    =				hidden_act
        A    =				hidden_dropout_prob
        A    =				attention_probs_dropout_prob
        A    =				initializer_range
        A    =				num_labels
        A    =				scope
        A    =				is_hybrid
        # sequence length of DPT = num_patches + 1 (we add 1 for the [CLS] token)
        A    =				(image_size // patch_size) ** 2
        A    =				num_patches + 1







  def 	UpperCamelCase       ( self	: List[Any] ):
        A    =				floats_tensor([self.batch_size, self.num_channels, self.image_size, self.image_size] )

        A    =				None
        if self.use_labels:
              A    =				ids_tensor([self.batch_size, self.image_size, self.image_size]		,						self.num_labels )

        A    =				self.get_config()

        return config, pixel_values, labels







  def 	UpperCamelCase       ( self	: List[Any] ):
        return DPTConfig(
            image_size=self.image_size		,						patch_size=self.patch_size		,						num_channels=self.num_channels		,						hidden_size=self.hidden_size		,						num_hidden_layers=self.num_hidden_layers		,						backbone_out_indices=self.backbone_out_indices		,						num_attention_heads=self.num_attention_heads		,						intermediate_size=self.intermediate_size		,						hidden_act=self.hidden_act		,						hidden_dropout_prob=self.hidden_dropout_prob		,						attention_probs_dropout_prob=self.attention_probs_dropout_prob		,						is_decoder=lowerCAmelCase_		,						initializer_range=self.initializer_range		,						is_hybrid=self.is_hybrid		,						)







  def 	UpperCamelCase       ( self	: List[str]		,						UpperCamelCase__	: Optional[int]		,						UpperCamelCase__	: Tuple		,						UpperCamelCase__	: str ):
        A    =				DPTModel(config=lowerCAmelCase_ )
        model.to(lowerCAmelCase_ )
        model.eval()
        A    =				model(lowerCAmelCase_ )
        self.parent.assertEqual(result.last_hidden_state.shape		,						(self.batch_size, self.seq_length, self.hidden_size) )







  def 	UpperCamelCase       ( self	: Tuple		,						UpperCamelCase__	: Union[str, Any]		,						UpperCamelCase__	: Optional[int]		,						UpperCamelCase__	: Optional[Any] ):
        A    =				self.num_labels
        A    =				DPTForDepthEstimation(lowerCAmelCase_ )
        model.to(lowerCAmelCase_ )
        model.eval()
        A    =				model(lowerCAmelCase_ )
        self.parent.assertEqual(result.predicted_depth.shape		,						(self.batch_size, self.image_size, self.image_size) )







  def 	UpperCamelCase       ( self	: Tuple		,						UpperCamelCase__	: str		,						UpperCamelCase__	: Any		,						UpperCamelCase__	: Union[str, Any] ):
        A    =				self.num_labels
        A    =				DPTForSemanticSegmentation(lowerCAmelCase_ )
        model.to(lowerCAmelCase_ )
        model.eval()
        A    =				model(lowerCAmelCase_		,						labels=lowerCAmelCase_ )
        self.parent.assertEqual(
            result.logits.shape		,						(self.batch_size, self.num_labels, self.image_size, self.image_size) )







  def 	UpperCamelCase       ( self	: int ):
        A    =				self.prepare_config_and_inputs()
        A ,	A ,	A    =				config_and_inputs
        A    =				{'pixel_values': pixel_values}
        return config, inputs_dict



@require_torch
class        _UpperCAmelCase (   lowerCAmelCase__     ,				lowerCAmelCase__     ,				unittest.TestCase			):
  '''simple docstring'''







  SCREAMING_SNAKE_CASE							:				Any					      =				(DPTModel, DPTForDepthEstimation, DPTForSemanticSegmentation) if is_torch_available() else ()
  SCREAMING_SNAKE_CASE							:				Any					      =				(
      {
          """depth-estimation""": DPTForDepthEstimation,
          """feature-extraction""": DPTModel,
          """image-segmentation""": DPTForSemanticSegmentation,
      }
      if is_torch_available()
      else {}
  )

  SCREAMING_SNAKE_CASE							:				Optional[Any]					      =				False
  SCREAMING_SNAKE_CASE							:				Tuple					      =				False
  SCREAMING_SNAKE_CASE							:				Any					      =				False







  def 	UpperCamelCase       ( self	: str ):
        A    =				DPTModelTester(self )
        A    =				ConfigTester(self		,						config_class=lowerCAmelCase_		,						has_text_modality=lowerCAmelCase_		,						hidden_size=37 )







  def 	UpperCamelCase       ( self	: int ):
        self.config_tester.run_common_tests()







  @unittest.skip(reason='DPT does not use inputs_embeds' )
  def 	UpperCamelCase       ( self	: Dict ):
        pass







  def 	UpperCamelCase       ( self	: str ):
        A ,	A    =				self.model_tester.prepare_config_and_inputs_for_common()

        for model_class in self.all_model_classes:
              A    =				model_class(lowerCAmelCase_ )
              self.assertIsInstance(model.get_input_embeddings()		,						(nn.Module) )
              A    =				model.get_output_embeddings()
              self.assertTrue(x is None or isinstance(lowerCAmelCase_		,						nn.Linear ) )







  def 	UpperCamelCase       ( self	: Union[str, Any] ):
        A ,	A    =				self.model_tester.prepare_config_and_inputs_for_common()

        for model_class in self.all_model_classes:
              A    =				model_class(lowerCAmelCase_ )
              A    =				inspect.signature(model.forward )
              # signature.parameters is an OrderedDict => so arg_names order is deterministic
              A    =				[*signature.parameters.keys()]

              A    =				['pixel_values']
              self.assertListEqual(arg_names[:1]		,						lowerCAmelCase_ )







  def 	UpperCamelCase       ( self	: Dict ):
        A    =				self.model_tester.prepare_config_and_inputs()
        self.model_tester.create_and_check_model(*lowerCAmelCase_ )







  def 	UpperCamelCase       ( self	: Optional[int] ):
        A    =				self.model_tester.prepare_config_and_inputs()
        self.model_tester.create_and_check_for_depth_estimation(*lowerCAmelCase_ )







  def 	UpperCamelCase       ( self	: Any ):
        A    =				self.model_tester.prepare_config_and_inputs()
        self.model_tester.create_and_check_for_semantic_segmentation(*lowerCAmelCase_ )







  def 	UpperCamelCase       ( self	: Optional[int] ):






        for model_class in self.all_model_classes:
              if model_class.__name__ == "DPTForDepthEstimation":
                    continue

              A ,	A    =				self.model_tester.prepare_config_and_inputs_for_common()
              A    =				True

              if model_class in get_values(lowerCAmelCase_ ):
                    continue

              A    =				model_class(lowerCAmelCase_ )
              model.to(lowerCAmelCase_ )
              model.train()
              A    =				self._prepare_for_class(lowerCAmelCase_		,						lowerCAmelCase_		,						return_labels=lowerCAmelCase_ )
              A    =				model(**lowerCAmelCase_ ).loss
              loss.backward()







  def 	UpperCamelCase       ( self	: str ):






        for model_class in self.all_model_classes:
              if model_class.__name__ == "DPTForDepthEstimation":
                    continue

              A ,	A    =				self.model_tester.prepare_config_and_inputs_for_common()
              A    =				False
              A    =				True

              if model_class in get_values(lowerCAmelCase_ ) or not model_class.supports_gradient_checkpointing:
                    continue
              A    =				model_class(lowerCAmelCase_ )
              model.to(lowerCAmelCase_ )
              model.gradient_checkpointing_enable()
              model.train()
              A    =				self._prepare_for_class(lowerCAmelCase_		,						lowerCAmelCase_		,						return_labels=lowerCAmelCase_ )
              A    =				model(**lowerCAmelCase_ ).loss
              loss.backward()







  def 	UpperCamelCase       ( self	: Dict ):
        A ,	A    =				self.model_tester.prepare_config_and_inputs_for_common()

        A    =				_config_zero_init(lowerCAmelCase_ )
        for model_class in self.all_model_classes:
              A    =				model_class(config=lowerCAmelCase_ )
              # Skip the check for the backbone
              A    =				[]
              for name, module in model.named_modules():
                    if module.__class__.__name__ == "DPTViTHybridEmbeddings":
                          A    =				[f'''{name}.{key}''' for key in module.state_dict().keys()]
                          break

              for name, param in model.named_parameters():
                    if param.requires_grad:
                          if name in backbone_params:
                                continue
                          self.assertIn(
                              ((param.data.mean() * 1e9).round() / 1e9).item()		,						[0.0, 1.0]		,						msg=f'''Parameter {name} of model {model_class} seems not properly initialized'''		,						)







  @unittest.skip('Will be fixed soon by reducing the size of the model used for common tests.' )
  def 	UpperCamelCase       ( self	: int ):
        pass







  @slow
  def 	UpperCamelCase       ( self	: Union[str, Any] ):






        for model_name in DPT_PRETRAINED_MODEL_ARCHIVE_LIST[:1]:
              A    =				DPTModel.from_pretrained(lowerCAmelCase_ )
              self.assertIsNotNone(lowerCAmelCase_ )


def 			__UpperCamelCase    ()     ->  Dict:
      A    =				Image.open('./tests/fixtures/tests_samples/COCO/000000039769.png'     )
      return image







@require_torch
@require_vision
@slow
class        _UpperCAmelCase (   unittest.TestCase			):
  '''simple docstring'''







  def 	UpperCamelCase       ( self	: Union[str, Any] ):
        A    =				DPTImageProcessor.from_pretrained('Intel/dpt-large' )
        A    =				DPTForDepthEstimation.from_pretrained('Intel/dpt-large' ).to(lowerCAmelCase_ )

        A    =				prepare_img()
        A    =				image_processor(images=lowerCAmelCase_		,						return_tensors='pt' ).to(lowerCAmelCase_ )

        # forward pass
        with torch.no_grad():
              A    =				model(**lowerCAmelCase_ )
              A    =				outputs.predicted_depth

        # verify the predicted depth
        A    =				torch.Size((1, 384, 384) )
        self.assertEqual(predicted_depth.shape		,						lowerCAmelCase_ )

        A    =				torch.tensor(
            [[6.3_199, 6.3_629, 6.4_148], [6.3_850, 6.3_615, 6.4_166], [6.3_519, 6.3_176, 6.3_575]] ).to(lowerCAmelCase_ )

        self.assertTrue(torch.allclose(outputs.predicted_depth[0, :3, :3]		,						lowerCAmelCase_		,						atol=1e-4 ) )







  def 	UpperCamelCase       ( self	: List[str] ):
        A    =				DPTImageProcessor.from_pretrained('Intel/dpt-large-ade' )
        A    =				DPTForSemanticSegmentation.from_pretrained('Intel/dpt-large-ade' ).to(lowerCAmelCase_ )

        A    =				prepare_img()
        A    =				image_processor(images=lowerCAmelCase_		,						return_tensors='pt' ).to(lowerCAmelCase_ )

        # forward pass
        with torch.no_grad():
              A    =				model(**lowerCAmelCase_ )

        # verify the logits
        A    =				torch.Size((1, 150, 480, 480) )
        self.assertEqual(outputs.logits.shape		,						lowerCAmelCase_ )

        A    =				torch.tensor(
            [[4.0_480, 4.2_420, 4.4_360], [4.3_124, 4.5_693, 4.8_261], [4.5_768, 4.8_965, 5.2_163]] ).to(lowerCAmelCase_ )

        self.assertTrue(torch.allclose(outputs.logits[0, 0, :3, :3]		,						lowerCAmelCase_		,						atol=1e-4 ) )







  def 	UpperCamelCase       ( self	: List[str] ):
        A    =				DPTImageProcessor.from_pretrained('Intel/dpt-large-ade' )
        A    =				DPTForSemanticSegmentation.from_pretrained('Intel/dpt-large-ade' ).to(lowerCAmelCase_ )

        A    =				prepare_img()
        A    =				image_processor(images=lowerCAmelCase_		,						return_tensors='pt' ).to(lowerCAmelCase_ )

        # forward pass
        with torch.no_grad():
              A    =				model(**lowerCAmelCase_ )

        A    =				outputs.logits.detach().cpu()

        A    =				image_processor.post_process_semantic_segmentation(outputs=lowerCAmelCase_		,						target_sizes=[(500, 300)] )
        A    =				torch.Size((500, 300) )
        self.assertEqual(segmentation[0].shape		,						lowerCAmelCase_ )

        A    =				image_processor.post_process_semantic_segmentation(outputs=lowerCAmelCase_ )
        A    =				torch.Size((480, 480) )
        self.assertEqual(segmentation[0].shape		,						lowerCAmelCase_ )






from math import floor, sqrt


def 			__UpperCamelCase    (lowerCAmelCase					:  int     )     ->  int:
      A    =				0.0
      A    =				1.0
      A    =				int(sqrt(lowerCAmelCase     )     )
      A    =				root
      A    =				0
      while integer_part != 2 * root:
            A    =				denominator * integer_part - numerator
            A    =				(n - numerator**2) / denominator
            A    =				int((root + numerator) / denominator     )
            period += 1
      return period


def 			__UpperCamelCase    (lowerCAmelCase					:  int = 10_000     )     ->  int:
      A    =				0
      for i in range(2,    n + 1     ):
            A    =				sqrt(lowerCAmelCase     )
            if sr - floor(lowerCAmelCase     ) != 0 and continuous_fraction_period(lowerCAmelCase     ) % 2 == 1:
                  count_odd_periods += 1
      return count_odd_periods


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



