
'''simple docstring'''




def 						lowerCAmelCase_							(  snake_case__ = 100_0000		):




    '''simple docstring'''



    A			:  Optional[int]   =		[i - 1 for i in range(limit + 1		)]

    for i in range(2						,							limit + 1		):
        if phi[i] == i - 1:
            for j in range(2 * i						,							limit + 1						,							snake_case__		):
                phi[j] -= phi[j] // i

    return sum(phi[2 : limit + 1]		)


if __name__ == "__main__":
      print(solution())






'''simple docstring'''




import inspect
import unittest

from transformers import ViTConfig
from transformers.testing_utils import (
    require_accelerate,
    require_torch,
    require_torch_gpu,
    require_vision,
    slow,
    torch_device,
)
from transformers.utils import cached_property, is_torch_available, is_vision_available

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


if is_torch_available():
      import torch
      from torch import nn

      from transformers import ViTForImageClassification, ViTForMaskedImageModeling, ViTModel
      from transformers.models.vit.modeling_vit import VIT_PRETRAINED_MODEL_ARCHIVE_LIST


if is_vision_available():
      from PIL import Image

      from transformers import ViTImageProcessor





class 					A							:





     def __init__(				self		,     SCREAMING_SNAKE_CASE		,     SCREAMING_SNAKE_CASE=13		,     SCREAMING_SNAKE_CASE=30		,     SCREAMING_SNAKE_CASE=2		,     SCREAMING_SNAKE_CASE=3		,     SCREAMING_SNAKE_CASE=True		,     SCREAMING_SNAKE_CASE=True		,     SCREAMING_SNAKE_CASE=32		,     SCREAMING_SNAKE_CASE=5		,     SCREAMING_SNAKE_CASE=4		,     SCREAMING_SNAKE_CASE=37		,     SCREAMING_SNAKE_CASE="gelu"		,     SCREAMING_SNAKE_CASE=0.1		,     SCREAMING_SNAKE_CASE=0.1		,     SCREAMING_SNAKE_CASE=10		,     SCREAMING_SNAKE_CASE=0.02		,     SCREAMING_SNAKE_CASE=None		,     SCREAMING_SNAKE_CASE=2		,     )					->							Any:






         """simple docstring"""






         A			:  Union[str, Any]   =		parent
         A			:  Optional[Any]   =		batch_size
         A			:  Tuple   =		image_size
         A			:  str   =		patch_size
         A			:  Dict   =		num_channels
         A			:  Tuple   =		is_training
         A			:  List[Any]   =		use_labels
         A			:  Optional[Any]   =		hidden_size
         A			:  Dict   =		num_hidden_layers
         A			:  Union[str, Any]   =		num_attention_heads
         A			:  List[Any]   =		intermediate_size
         A			:  Any   =		hidden_act
         A			:  Dict   =		hidden_dropout_prob
         A			:  Any   =		attention_probs_dropout_prob
         A			:  Dict   =		type_sequence_label_size
         A			:  List[Any]   =		initializer_range
         A			:  Dict   =		scope
         A			:  Any   =		encoder_stride

         # in ViT, the seq length equals the number of patches + 1 (we add 1 for the [CLS] token)
         A			:  int   =		(image_size // patch_size) ** 2
         A			:  Optional[Any]   =		num_patches + 1





     def 							__lowerCAmelCase				(				self      )					->							Optional[int]:






         """simple docstring"""






         A			:  List[str]   =		floats_tensor([self.batch_size, self.num_channels, self.image_size, self.image_size]      )

         A			:  str   =		None
         if self.use_labels:
             A			:  str   =		ids_tensor([self.batch_size]		,     self.type_sequence_label_size      )

         A			:  Dict   =		self.get_config()

         return config, pixel_values, labels





     def 							__lowerCAmelCase				(				self      )					->							Any:






         """simple docstring"""






         return ViTConfig(
             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		,     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=SCREAMING_SNAKE_CASE		,     initializer_range=self.initializer_range		,     encoder_stride=self.encoder_stride		,     )





     def 							__lowerCAmelCase				(				self		,     SCREAMING_SNAKE_CASE		,     SCREAMING_SNAKE_CASE		,     SCREAMING_SNAKE_CASE      )					->							int:






         """simple docstring"""






         A			:  str   =		ViTModel(config=SCREAMING_SNAKE_CASE      )
         model.to(SCREAMING_SNAKE_CASE      )
         model.eval()
         A			:  Optional[Any]   =		model(SCREAMING_SNAKE_CASE      )
         self.parent.assertEqual(result.last_hidden_state.shape		,     (self.batch_size, self.seq_length, self.hidden_size)      )





     def 							__lowerCAmelCase				(				self		,     SCREAMING_SNAKE_CASE		,     SCREAMING_SNAKE_CASE		,     SCREAMING_SNAKE_CASE      )					->							Any:






         """simple docstring"""






         A			:  Any   =		ViTForMaskedImageModeling(config=SCREAMING_SNAKE_CASE      )
         model.to(SCREAMING_SNAKE_CASE      )
         model.eval()
         A			:  Any   =		model(SCREAMING_SNAKE_CASE      )
         self.parent.assertEqual(
             result.reconstruction.shape		,     (self.batch_size, self.num_channels, self.image_size, self.image_size)      )

         # test greyscale images
         A			:  Optional[Any]   =		1
         A			:  str   =		ViTForMaskedImageModeling(SCREAMING_SNAKE_CASE      )
         model.to(SCREAMING_SNAKE_CASE      )
         model.eval()

         A			:  List[str]   =		floats_tensor([self.batch_size, 1, self.image_size, self.image_size]      )
         A			:  Union[str, Any]   =		model(SCREAMING_SNAKE_CASE      )
         self.parent.assertEqual(result.reconstruction.shape		,     (self.batch_size, 1, self.image_size, self.image_size)      )





     def 							__lowerCAmelCase				(				self		,     SCREAMING_SNAKE_CASE		,     SCREAMING_SNAKE_CASE		,     SCREAMING_SNAKE_CASE      )					->							int:






         """simple docstring"""






         A			:  str   =		self.type_sequence_label_size
         A			:  Optional[int]   =		ViTForImageClassification(SCREAMING_SNAKE_CASE      )
         model.to(SCREAMING_SNAKE_CASE      )
         model.eval()
         A			:  List[Any]   =		model(SCREAMING_SNAKE_CASE		,     labels=SCREAMING_SNAKE_CASE      )
         self.parent.assertEqual(result.logits.shape		,     (self.batch_size, self.type_sequence_label_size)      )

         # test greyscale images
         A			:  int   =		1
         A			:  Any   =		ViTForImageClassification(SCREAMING_SNAKE_CASE      )
         model.to(SCREAMING_SNAKE_CASE      )
         model.eval()

         A			:  Dict   =		floats_tensor([self.batch_size, 1, self.image_size, self.image_size]      )
         A			:  str   =		model(SCREAMING_SNAKE_CASE      )
         self.parent.assertEqual(result.logits.shape		,     (self.batch_size, self.type_sequence_label_size)      )





     def 							__lowerCAmelCase				(				self      )					->							Optional[int]:






         """simple docstring"""






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





@require_torch
class 					A							(				__snake_case       ,     __snake_case       ,     unittest.TestCase		):
     __magic_name__          =						(
         (
             ViTModel,
             ViTForImageClassification,
             ViTForMaskedImageModeling,
         )
         if is_torch_available()
         else ()
     )
     __magic_name__          =						(
         {'''feature-extraction''': ViTModel, '''image-classification''': ViTForImageClassification}
         if is_torch_available()
         else {}
     )
     __magic_name__          =						True

     __magic_name__          =						False
     __magic_name__          =						False
     __magic_name__          =						False





     def 							__lowerCAmelCase				(				self      )					->							Tuple:






         """simple docstring"""






         A			:  List[str]   =		ViTModelTester(self      )
         A			:  List[str]   =		ConfigTester(self		,     config_class=SCREAMING_SNAKE_CASE		,     has_text_modality=SCREAMING_SNAKE_CASE		,     hidden_size=37      )





     def 							__lowerCAmelCase				(				self      )					->							Optional[Any]:






         """simple docstring"""






         self.config_tester.run_common_tests()





     @unittest.skip(reason='''ViT does not use inputs_embeds'''      )
     def 							__lowerCAmelCase				(				self      )					->							Dict:






         """simple docstring"""






         pass





     def 							__lowerCAmelCase				(				self      )					->							int:






         """simple docstring"""






         A,    A			:  List[Any]   =		self.model_tester.prepare_config_and_inputs_for_common()

         for model_class in self.all_model_classes:
             A			:  Any   =		model_class(SCREAMING_SNAKE_CASE      )
             self.assertIsInstance(model.get_input_embeddings()		,     (nn.Module)      )
             A			:  Optional[int]   =		model.get_output_embeddings()
             self.assertTrue(x is None or isinstance(SCREAMING_SNAKE_CASE		,     nn.Linear      )      )





     def 							__lowerCAmelCase				(				self      )					->							Optional[int]:






         """simple docstring"""






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

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

             A			:  Optional[int]   =		['''pixel_values''']
             self.assertListEqual(arg_names[:1]		,     SCREAMING_SNAKE_CASE      )





     def 							__lowerCAmelCase				(				self      )					->							Optional[int]:






         """simple docstring"""






         A			:  Optional[Any]   =		self.model_tester.prepare_config_and_inputs()
         self.model_tester.create_and_check_model(*SCREAMING_SNAKE_CASE      )





     def 							__lowerCAmelCase				(				self      )					->							Optional[int]:






         """simple docstring"""






         A			:  Union[str, Any]   =		self.model_tester.prepare_config_and_inputs()
         self.model_tester.create_and_check_for_masked_image_modeling(*SCREAMING_SNAKE_CASE      )





     def 							__lowerCAmelCase				(				self      )					->							Any:






         """simple docstring"""






         A			:  Optional[Any]   =		self.model_tester.prepare_config_and_inputs()
         self.model_tester.create_and_check_for_image_classification(*SCREAMING_SNAKE_CASE      )





     @slow
     def 							__lowerCAmelCase				(				self      )					->							List[str]:






         """simple docstring"""






         for model_name in VIT_PRETRAINED_MODEL_ARCHIVE_LIST[:1]:
             A			:  Optional[Any]   =		ViTModel.from_pretrained(SCREAMING_SNAKE_CASE      )
             self.assertIsNotNone(SCREAMING_SNAKE_CASE      )







def 						lowerCAmelCase_							(  ):




    '''simple docstring'''



    A			:  Optional[int]   =		Image.open('''./tests/fixtures/tests_samples/COCO/000000039769.png'''		)
    return image







@require_torch
@require_vision
class 					A							(				unittest.TestCase		):





     @cached_property
     def 							__lowerCAmelCase				(				self      )					->							Union[str, Any]:






         """simple docstring"""






         return ViTImageProcessor.from_pretrained('''google/vit-base-patch16-224'''      ) if is_vision_available() else None





     @slow
     def 							__lowerCAmelCase				(				self      )					->							Any:






         """simple docstring"""






         A			:  List[Any]   =		ViTForImageClassification.from_pretrained('''google/vit-base-patch16-224'''      ).to(SCREAMING_SNAKE_CASE      )

         A			:  Optional[int]   =		self.default_image_processor
         A			:  int   =		prepare_img()
         A			:  Tuple   =		image_processor(images=SCREAMING_SNAKE_CASE		,     return_tensors='''pt'''      ).to(SCREAMING_SNAKE_CASE      )

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

         # verify the logits
         A			:  List[Any]   =		torch.Size((1, 1000)      )
         self.assertEqual(outputs.logits.shape		,     SCREAMING_SNAKE_CASE      )

         A			:  List[str]   =		torch.tensor([-0.2_744, 0.8_215, -0.0_836]      ).to(SCREAMING_SNAKE_CASE      )

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





     @slow
     def 							__lowerCAmelCase				(				self      )					->							Union[str, Any]:






         """simple docstring"""






         A			:  Dict   =		ViTModel.from_pretrained('''facebook/dino-vits8'''      ).to(SCREAMING_SNAKE_CASE      )

         A			:  int   =		ViTImageProcessor.from_pretrained('''facebook/dino-vits8'''		,     size=480      )
         A			:  Tuple   =		prepare_img()
         A			:  List[Any]   =		image_processor(images=SCREAMING_SNAKE_CASE		,     return_tensors='''pt'''      )
         A			:  Tuple   =		inputs.pixel_values.to(SCREAMING_SNAKE_CASE      )

         # forward pass
         with torch.no_grad():
             A			:  Any   =		model(SCREAMING_SNAKE_CASE		,     interpolate_pos_encoding=SCREAMING_SNAKE_CASE      )

         # verify the logits
         A			:  int   =		torch.Size((1, 3601, 384)      )
         self.assertEqual(outputs.last_hidden_state.shape		,     SCREAMING_SNAKE_CASE      )

         A			:  Union[str, Any]   =		torch.tensor(
             [[4.2_340, 4.3_906, -6.6_692], [4.5_463, 1.8_928, -6.7_257], [4.4_429, 0.8_496, -5.8_585]]      ).to(SCREAMING_SNAKE_CASE      )

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





     @slow
     @require_accelerate
     @require_torch_gpu
     def 							__lowerCAmelCase				(				self      )					->							Union[str, Any]:






         """simple docstring"""






         A			:  List[Any]   =		ViTModel.from_pretrained('''facebook/dino-vits8'''		,     torch_dtype=torch.floataa		,     device_map='''auto'''      )
         A			:  int   =		self.default_image_processor

         A			:  List[str]   =		prepare_img()
         A			:  Union[str, Any]   =		image_processor(images=SCREAMING_SNAKE_CASE		,     return_tensors='''pt'''      )
         A			:  List[Any]   =		inputs.pixel_values.to(SCREAMING_SNAKE_CASE      )

         # forward pass to make sure inference works in fp16
         with torch.no_grad():
             A			:  str   =		model(SCREAMING_SNAKE_CASE      )




