code: 
  
  
  """simple docstring"""
  
  
  
  
  
  
  
  import unittest
  
  import numpy as np
  import PIL
  import torch
  
  from diffusers.image_processor import VaeImageProcessor
  
  
  
  
  
  
  class    __A       ( unittest.TestCase    ):
  
  
  
  
  
  
   """simple docstring"""
  
  
  
  
   @property
   def    SCREAMING_SNAKE_CASE							(	self		)      ->  List[str]:
       a					=1
       a					=3
       a					=8
       a					=8
  
       a					=torch.rand((batch_size, num_channels, height, width)		)
  
       return sample
  
  
   def    SCREAMING_SNAKE_CASE							(	self				,					__A		)      ->  List[str]:
  
  
       if isinstance(image[0]				,					PIL.Image.Image		):
           return np.stack([np.array(__UpperCamelCase		) for i in image]				,					axis=0		)
       elif isinstance(__UpperCamelCase				,					torch.Tensor		):
           return image.cpu().numpy().transpose(0				,					2				,					3				,					1		)
       return image
  
  
   def    SCREAMING_SNAKE_CASE							(	self		)      ->  int:
       a					=VaeImageProcessor(do_resize=__UpperCamelCase				,					do_normalize=__UpperCamelCase		)
  
       a					=self.dummy_sample
       a					=self.to_np(__UpperCamelCase		)
  
       for output_type in ["pt", "np", "pil"]:
           a					=image_processor.postprocess(
               image_processor.preprocess(__UpperCamelCase		)				,					output_type=__UpperCamelCase				,					)
           a					=self.to_np(__UpperCamelCase		)
           a					=(input_np * 255).round() if output_type == '''pil''' else input_np
           assert (
               np.abs(in_np - out_np		).max() < 1E-6
           ), f'''decoded output does not match input for output_type {output_type}'''
  
  
   def    SCREAMING_SNAKE_CASE							(	self		)      ->  Any:
       a					=VaeImageProcessor(do_resize=__UpperCamelCase				,					do_normalize=__UpperCamelCase		)
       a					=self.dummy_sample.cpu().numpy().transpose(0				,					2				,					3				,					1		)
  
       for output_type in ["pt", "np", "pil"]:
           a					=image_processor.postprocess(image_processor.preprocess(__UpperCamelCase		)				,					output_type=__UpperCamelCase		)
  
           a					=self.to_np(__UpperCamelCase		)
           a					=(input_np * 255).round() if output_type == '''pil''' else input_np
           assert (
               np.abs(in_np - out_np		).max() < 1E-6
           ), f'''decoded output does not match input for output_type {output_type}'''
  
  
   def    SCREAMING_SNAKE_CASE							(	self		)      ->  Union[str, Any]:
       a					=VaeImageProcessor(do_resize=__UpperCamelCase				,					do_normalize=__UpperCamelCase		)
  
       a					=self.dummy_sample.cpu().numpy().transpose(0				,					2				,					3				,					1		)
       a					=image_processor.numpy_to_pil(__UpperCamelCase		)
  
       for output_type in ["pt", "np", "pil"]:
           a					=image_processor.postprocess(image_processor.preprocess(__UpperCamelCase		)				,					output_type=__UpperCamelCase		)
           for i, o in zip(__UpperCamelCase				,					__UpperCamelCase		):
               a					=np.array(__UpperCamelCase		)
               a					=self.to_np(__UpperCamelCase		) if output_type == '''pil''' else (self.to_np(__UpperCamelCase		) * 255).round()
               assert (
                   np.abs(in_np - out_np		).max() < 1E-6
               ), f'''decoded output does not match input for output_type {output_type}'''
  
  
   def    SCREAMING_SNAKE_CASE							(	self		)      ->  Union[str, Any]:
       a					=VaeImageProcessor(do_resize=__UpperCamelCase				,					do_normalize=__UpperCamelCase		)
  
       a					=self.dummy_sample
       a					=input_pt_ad.squeeze(0		)
  
       a					=image_processor.postprocess(
           image_processor.preprocess(__UpperCamelCase		)				,					output_type='''np'''				,					)
       a					=image_processor.postprocess(
           image_processor.preprocess(__UpperCamelCase		)				,					output_type='''np'''				,					)
  
       a					=self.to_np(self.dummy_sample		)
       a					=input_np_ad.squeeze(0		)
  
       a					=image_processor.postprocess(
           image_processor.preprocess(__UpperCamelCase		)				,					output_type='''np'''				,					)
       a					=image_processor.postprocess(
           image_processor.preprocess(__UpperCamelCase		)				,					output_type='''np'''				,					)
  
       assert np.abs(out_pt_ad - out_pt_ad		).max() < 1E-6
       assert np.abs(out_np_ad - out_np_ad		).max() < 1E-6
  
  
  
  
  
   def    SCREAMING_SNAKE_CASE							(	self		)      ->  List[str]:
       a					=VaeImageProcessor(do_resize=__UpperCamelCase				,					do_normalize=__UpperCamelCase		)
  
       a					=self.dummy_sample
       a					=list(__UpperCamelCase		)
  
       a					=image_processor.postprocess(
           image_processor.preprocess(__UpperCamelCase		)				,					output_type='''np'''				,					)
  
       a					=image_processor.postprocess(
           image_processor.preprocess(__UpperCamelCase		)				,					output_type='''np'''				,					)
  
       a					=self.to_np(self.dummy_sample		)
       list(__UpperCamelCase		)
  
       a					=image_processor.postprocess(
           image_processor.preprocess(__UpperCamelCase		)				,					output_type='''np'''				,					)
  
       a					=image_processor.postprocess(
           image_processor.preprocess(__UpperCamelCase		)				,					output_type='''np'''				,					)
  
       assert np.abs(out_pt_ad - out_pt_list		).max() < 1E-6
       assert np.abs(out_np_ad - out_np_list		).max() < 1E-6
style_context: 
  
  
  """simple docstring"""
  
  
  
  
  
  
  
  from math import gcd
  def _A		(		lowercase = 1_20_00	):
  
  
  
  
  
  
  
      """simple docstring"""
      a					=0
      for d in range(max_d + 1	):
          for n in range(d // 3 + 1 ,					(d + 1) // 2	):
              if gcd(lowercase ,					lowercase	) == 1:
                  fractions_number += 1
      return fractions_number
  
  
  if __name__ == "__main__":
         print(F'{solution() = }')