
"""simple docstring"""

import unittest

import torch

from diffusers import DDIMScheduler, DDPMScheduler, UNetaDModel
from diffusers.training_utils import set_seed
from diffusers.utils.testing_utils import slow


SCREAMING_SNAKE_CASE_            =    False
class   _UpperCAmelCase				(		unittest.TestCase				):




      def      a_   (				self ,							lowercase_=3_2				)    ->       int:
          set_seed(0				)
          UpperCAmelCase          =       UNetaDModel(sample_size=lowercase_ ,							in_channels=3 ,							out_channels=3				)
          UpperCAmelCase          =       torch.optim.SGD(model.parameters() ,							lr=0.0_0_0_1				)
          return model, optimizer




      @slow
      def      a_   (				self				)    ->       List[str]:
          UpperCAmelCase          =       'cpu'  # ensure full determinism without setting the CUBLAS_WORKSPACE_CONFIG env variable
          UpperCAmelCase          =       DDPMScheduler(
              num_train_timesteps=1_0_0_0 ,							beta_start=0.0_0_0_1 ,							beta_end=0.0_2 ,							beta_schedule='linear' ,							clip_sample=lowercase_ ,							)
          UpperCAmelCase          =       DDIMScheduler(
              num_train_timesteps=1_0_0_0 ,							beta_start=0.0_0_0_1 ,							beta_end=0.0_2 ,							beta_schedule='linear' ,							clip_sample=lowercase_ ,							)

          assert ddpm_scheduler.config.num_train_timesteps == ddim_scheduler.config.num_train_timesteps

          # shared batches for DDPM and DDIM
          set_seed(0				)
          UpperCAmelCase          =       [torch.randn((4, 3, 3_2, 3_2)				).clip(-1 ,							1				).to(lowercase_				) for _ in range(4				)]
          UpperCAmelCase          =       [torch.randn((4, 3, 3_2, 3_2)				).to(lowercase_				) for _ in range(4				)]
          UpperCAmelCase          =       [torch.randint(0 ,							1_0_0_0 ,							(4,)				).long().to(lowercase_				) for _ in range(4				)]

          # train with a DDPM scheduler
          UpperCAmelCase      ,				UpperCAmelCase          =       self.get_model_optimizer(resolution=3_2				)
          model.train().to(lowercase_				)
          for i in range(4				):
              optimizer.zero_grad()
              UpperCAmelCase          =       ddpm_scheduler.add_noise(clean_images[i] ,							noise[i] ,							timesteps[i]				)
              UpperCAmelCase          =       model(lowercase_ ,							timesteps[i]				).sample
              UpperCAmelCase          =       torch.nn.functional.mse_loss(lowercase_ ,							noise[i]				)
              loss.backward()
              optimizer.step()
          del model, optimizer

          # recreate the model and optimizer, and retry with DDIM
          UpperCAmelCase      ,				UpperCAmelCase          =       self.get_model_optimizer(resolution=3_2				)
          model.train().to(lowercase_				)
          for i in range(4				):
              optimizer.zero_grad()
              UpperCAmelCase          =       ddim_scheduler.add_noise(clean_images[i] ,							noise[i] ,							timesteps[i]				)
              UpperCAmelCase          =       model(lowercase_ ,							timesteps[i]				).sample
              UpperCAmelCase          =       torch.nn.functional.mse_loss(lowercase_ ,							noise[i]				)
              loss.backward()
              optimizer.step()
          del model, optimizer

          self.assertTrue(torch.allclose(lowercase_ ,							lowercase_ ,							atol=1E-5				)				)
          self.assertTrue(torch.allclose(lowercase_ ,							lowercase_ ,							atol=1E-5				)				)





"""simple docstring"""

from math import ceil, sqrt




def      lowercase__    (       lowerCAmelCase					:       int = 1_000_000			)			->   int:






    """simple docstring"""




    UpperCAmelCase          =       0

    for outer_width in range(3			,					(limit // 4) + 2			):
        if outer_width**2 > limit:
            UpperCAmelCase          =       max(ceil(sqrt(outer_width**2 - limit			)			)			,					1			)
        else:
            UpperCAmelCase          =       1
        if (outer_width - hole_width_lower_bound) % 2:
            hole_width_lower_bound += 1

        answer += (outer_width - hole_width_lower_bound - 2) // 2 + 1

    return answer


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



