





def _A       (   __magic_name__ = 100_0000	):
   lowercase__			       =  limit + 1
   lowercase__			       =  [0] * limit
   for first_term in range(1  , __magic_name__	):
      for n in range(__magic_name__  , __magic_name__  , __magic_name__	):
         lowercase__			       =  first_term + n / first_term
         if common_difference % 4:  # d must be divisble by 4
            continue
         else:
            common_difference /= 4
            if (
                first_term > common_difference
                and first_term < 4 * common_difference
            ):  # since x,y,z are positive integers
               frequency[n] += 1  # so z>0 and a>d ,also 4d<a

   lowercase__			       =  sum(1 for x in frequency[1:limit] if x == 10	)

   return count


if __name__ == "__main__":
  print(F"""{solution() = }""")













import gc
import random
import unittest

import numpy as np
import torch
from transformers import CLIPTextConfig, CLIPTextModel, CLIPTokenizer

import diffusers
from diffusers import (
    AutoencoderKL,
    EulerDiscreteScheduler,
    StableDiffusionLatentUpscalePipeline,
    StableDiffusionPipeline,
    UNetaDConditionModel,
)
from diffusers.schedulers import KarrasDiffusionSchedulers
from diffusers.utils import floats_tensor, load_image, load_numpy, slow, torch_device
from diffusers.utils.testing_utils import enable_full_determinism, require_torch_gpu

from ..pipeline_params import TEXT_GUIDED_IMAGE_VARIATION_BATCH_PARAMS, TEXT_GUIDED_IMAGE_VARIATION_PARAMS
from ..test_pipelines_common import PipelineKarrasSchedulerTesterMixin, PipelineLatentTesterMixin, PipelineTesterMixin


enable_full_determinism()


def _A       (   __magic_name__	):
   lowercase__			       =  [tensor.shape for tensor in tensor_list]
   return all(shape == shapes[0] for shape in shapes[1:]	)





class  lowerCAmelCase							(       lowercase_							,							lowercase_							,							lowercase_							,							unittest.TestCase ):
  __lowerCamelCase		=      StableDiffusionLatentUpscalePipeline
  __lowerCamelCase		=      TEXT_GUIDED_IMAGE_VARIATION_PARAMS - {
      'height',
      'width',
      'cross_attention_kwargs',
      'negative_prompt_embeds',
      'prompt_embeds',
  }
  __lowerCamelCase		=      PipelineTesterMixin.required_optional_params - {'num_images_per_prompt'}
  __lowerCamelCase		=      TEXT_GUIDED_IMAGE_VARIATION_BATCH_PARAMS
  __lowerCamelCase		=      frozenset(
      [] )  # TO-DO: update image_params once pipeline is refactored with VaeImageProcessor.preprocess
  __lowerCamelCase		=      frozenset([] )

  __lowerCamelCase		=      True







  @property
  def   UpperCAmelCase					(      self  :Optional[Any] ):






     '''simple docstring'''





     lowercase__			       =  1
     lowercase__			       =  4
     lowercase__			       =  (16, 16)

     lowercase__			       =  floats_tensor((batch_size, num_channels) + sizes   ,							rng=random.Random(0 ) ).to(_lowercase )
     return image







  def   UpperCAmelCase					(      self  :Dict ):






     '''simple docstring'''





     torch.manual_seed(0 )
     lowercase__			       =  UNetaDConditionModel(
         act_fn="gelu"   ,							attention_head_dim=8   ,							norm_num_groups=_lowercase   ,							block_out_channels=[32, 32, 64, 64]   ,							time_cond_proj_dim=1_60   ,							conv_in_kernel=1   ,							conv_out_kernel=1   ,							cross_attention_dim=32   ,							down_block_types=(
             "KDownBlock2D",
             "KCrossAttnDownBlock2D",
             "KCrossAttnDownBlock2D",
             "KCrossAttnDownBlock2D",
         )   ,							in_channels=8   ,							mid_block_type=_lowercase   ,							only_cross_attention=_lowercase   ,							out_channels=5   ,							resnet_time_scale_shift="scale_shift"   ,							time_embedding_type="fourier"   ,							timestep_post_act="gelu"   ,							up_block_types=("KCrossAttnUpBlock2D", "KCrossAttnUpBlock2D", "KCrossAttnUpBlock2D", "KUpBlock2D")   ,							)
     lowercase__			       =  AutoencoderKL(
         block_out_channels=[32, 32, 64, 64]   ,							in_channels=3   ,							out_channels=3   ,							down_block_types=[
             "DownEncoderBlock2D",
             "DownEncoderBlock2D",
             "DownEncoderBlock2D",
             "DownEncoderBlock2D",
         ]   ,							up_block_types=["UpDecoderBlock2D", "UpDecoderBlock2D", "UpDecoderBlock2D", "UpDecoderBlock2D"]   ,							latent_channels=4   ,							)
     lowercase__			       =  EulerDiscreteScheduler(prediction_type="sample" )
     lowercase__			       =  CLIPTextConfig(
         bos_token_id=0   ,							eos_token_id=2   ,							hidden_size=32   ,							intermediate_size=37   ,							layer_norm_eps=1e-05   ,							num_attention_heads=4   ,							num_hidden_layers=5   ,							pad_token_id=1   ,							vocab_size=10_00   ,							hidden_act="quick_gelu"   ,							projection_dim=5_12   ,							)
     lowercase__			       =  CLIPTextModel(_lowercase )
     lowercase__			       =  CLIPTokenizer.from_pretrained("hf-internal-testing/tiny-random-clip" )

     lowercase__			       =  {
         "unet": model.eval(),
         "vae": vae.eval(),
         "scheduler": scheduler,
         "text_encoder": text_encoder,
         "tokenizer": tokenizer,
     }

     return components







  def   UpperCAmelCase					(      self  :Dict   ,							_lowercase  :Union[str, Any]   ,							_lowercase  :int=0 ):






     '''simple docstring'''





     if str(_lowercase ).startswith("mps" ):
        lowercase__			       =  torch.manual_seed(_lowercase )
     else:
        lowercase__			       =  torch.Generator(device=_lowercase ).manual_seed(_lowercase )
     lowercase__			       =  {
         "prompt": "A painting of a squirrel eating a burger",
         "image": self.dummy_image.cpu(),
         "generator": generator,
         "num_inference_steps": 2,
         "output_type": "numpy",
     }
     return inputs







  def   UpperCAmelCase					(      self  :List[Any] ):






     '''simple docstring'''





     lowercase__			       =  "cpu"

     lowercase__			       =  self.get_dummy_components()
     lowercase__			       =  self.pipeline_class(**_lowercase )
     pipe.to(_lowercase )
     pipe.set_progress_bar_config(disable=_lowercase )

     lowercase__			       =  self.get_dummy_inputs(_lowercase )
     lowercase__			       =  pipe(**_lowercase ).images
     lowercase__			       =  image[0, -3:, -3:, -1]

     self.assertEqual(image.shape   ,							(1, 2_56, 2_56, 3) )
     lowercase__			       =  np.array(
         [0.47222412, 0.41921633, 0.44717434, 0.46874192, 0.42588258, 0.46150726, 0.4677534, 0.45583832, 0.48579055] )
     lowercase__			       =  np.abs(image_slice.flatten() - expected_slice ).max()
     self.assertLessEqual(_lowercase   ,							1e-3 )







  def   UpperCAmelCase					(      self  :Any ):






     '''simple docstring'''





     super().test_attention_slicing_forward_pass(expected_max_diff=7e-3 )







  def   UpperCAmelCase					(      self  :List[Any] ):






     '''simple docstring'''





     super().test_cpu_offload_forward_pass(expected_max_diff=3e-3 )







  def   UpperCAmelCase					(      self  :int ):






     '''simple docstring'''





     super().test_dict_tuple_outputs_equivalent(expected_max_difference=3e-3 )







  def   UpperCAmelCase					(      self  :List[Any] ):






     '''simple docstring'''





     super().test_inference_batch_single_identical(expected_max_diff=7e-3 )







  def   UpperCAmelCase					(      self  :List[Any] ):






     '''simple docstring'''





     super().test_pt_np_pil_outputs_equivalent(expected_max_diff=3e-3 )







  def   UpperCAmelCase					(      self  :Optional[int] ):






     '''simple docstring'''





     super().test_save_load_local(expected_max_difference=3e-3 )







  def   UpperCAmelCase					(      self  :Tuple ):






     '''simple docstring'''





     super().test_save_load_optional_components(expected_max_difference=3e-3 )







  def   UpperCAmelCase					(      self  :Dict ):






     '''simple docstring'''





     lowercase__			       =  [
         "DDIMScheduler",
         "DDPMScheduler",
         "PNDMScheduler",
         "HeunDiscreteScheduler",
         "EulerAncestralDiscreteScheduler",
         "KDPM2DiscreteScheduler",
         "KDPM2AncestralDiscreteScheduler",
         "DPMSolverSDEScheduler",
     ]
     lowercase__			       =  self.get_dummy_components()
     lowercase__			       =  self.pipeline_class(**_lowercase )

     # make sure that PNDM does not need warm-up
     pipe.scheduler.register_to_config(skip_prk_steps=_lowercase )

     pipe.to(_lowercase )
     pipe.set_progress_bar_config(disable=_lowercase )
     lowercase__			       =  self.get_dummy_inputs(_lowercase )
     lowercase__			       =  2

     lowercase__			       =  []
     for scheduler_enum in KarrasDiffusionSchedulers:
        if scheduler_enum.name in skip_schedulers:
           # no sigma schedulers are not supported
           # no schedulers
           continue

        lowercase__			       =  getattr(_lowercase   ,							scheduler_enum.name )
        lowercase__			       =  scheduler_cls.from_config(pipe.scheduler.config )
        lowercase__			       =  pipe(**_lowercase )[0]
        outputs.append(_lowercase )

     assert check_same_shape(_lowercase )





@require_torch_gpu
@slow
class  lowerCAmelCase							(       unittest.TestCase ):







  def   UpperCAmelCase					(      self  :Optional[Any] ):






     '''simple docstring'''





     super().tearDown()
     gc.collect()
     torch.cuda.empty_cache()







  def   UpperCAmelCase					(      self  :str ):






     '''simple docstring'''





     lowercase__			       =  torch.manual_seed(33 )

     lowercase__			       =  StableDiffusionPipeline.from_pretrained("CompVis/stable-diffusion-v1-4"   ,							torch_dtype=torch.floataa )
     pipe.to("cuda" )

     lowercase__			       =  StableDiffusionLatentUpscalePipeline.from_pretrained(
         "stabilityai/sd-x2-latent-upscaler"   ,							torch_dtype=torch.floataa )
     upscaler.to("cuda" )

     lowercase__			       =  "a photo of an astronaut high resolution, unreal engine, ultra realistic"

     lowercase__			       =  pipe(_lowercase   ,							generator=_lowercase   ,							output_type="latent" ).images

     lowercase__			       =  upscaler(
         prompt=_lowercase   ,							image=_lowercase   ,							num_inference_steps=20   ,							guidance_scale=0   ,							generator=_lowercase   ,							output_type="np"   ,							).images[0]

     lowercase__			       =  load_numpy(
         "https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main/latent-upscaler/astronaut_1024.npy" )
     assert np.abs((expected_image - image).mean() ) < 5e-2







  def   UpperCAmelCase					(      self  :Optional[Any] ):






     '''simple docstring'''





     lowercase__			       =  torch.manual_seed(33 )

     lowercase__			       =  StableDiffusionLatentUpscalePipeline.from_pretrained(
         "stabilityai/sd-x2-latent-upscaler"   ,							torch_dtype=torch.floataa )
     upscaler.to("cuda" )

     lowercase__			       =  "the temple of fire by Ross Tran and Gerardo Dottori, oil on canvas"

     lowercase__			       =  load_image(
         "https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main/latent-upscaler/fire_temple_512.png" )

     lowercase__			       =  upscaler(
         prompt=_lowercase   ,							image=_lowercase   ,							num_inference_steps=20   ,							guidance_scale=0   ,							generator=_lowercase   ,							output_type="np"   ,							).images[0]

     lowercase__			       =  load_numpy(
         "https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main/latent-upscaler/fire_temple_1024.npy" )
     assert np.abs((expected_image - image).max() ) < 5e-2






