





a_					      = 10**8





def      __lowercase  (		lowerCamelCase      :  int			):
 if n % 10 == 0:
  return False
 UpperCamelCase_      :		Optional[int]				=      str(lowerCamelCase			)
 return s == s[::-1]





def      __lowercase  (		):
 UpperCamelCase_      :		List[Any]				=      set()
 UpperCamelCase_      :		Any				=      1
 UpperCamelCase_      :		Any				=      5
 while sum_squares < LIMIT:
  UpperCamelCase_      :		Union[str, Any]				=      first_square + 1
  while sum_squares < LIMIT:
   if is_palindrome(lowerCamelCase			):
    answer.add(lowerCamelCase			)
   last_square += 1
   sum_squares += last_square**2
  first_square += 1
  UpperCamelCase_      :		Tuple				=      first_square**2 + (first_square + 1) ** 2

 return sum(lowerCamelCase			)


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




from typing import List, Optional, Union

import numpy as np
import PIL
import torch
from PIL import Image

from ...models import UNetaDConditionModel, VQModel
from ...pipelines import DiffusionPipeline
from ...pipelines.pipeline_utils import ImagePipelineOutput
from ...schedulers import DDPMScheduler
from ...utils import (
    is_accelerate_available,
    is_accelerate_version,
    logging,
    randn_tensor,
    replace_example_docstring,
)


a_					      = logging.get_logger(__name__)  # pylint: disable=invalid-name

a_					      = '\n    Examples:\n        ```py\n        >>> import torch\n        >>> import numpy as np\n\n        >>> from diffusers import KandinskyV22PriorEmb2EmbPipeline, KandinskyV22ControlnetImg2ImgPipeline\n        >>> from transformers import pipeline\n        >>> from diffusers.utils import load_image\n\n\n        >>> def make_hint(image, depth_estimator):\n        ...     image = depth_estimator(image)["depth"]\n        ...     image = np.array(image)\n        ...     image = image[:, :, None]\n        ...     image = np.concatenate([image, image, image], axis=2)\n        ...     detected_map = torch.from_numpy(image).float() / 255.0\n        ...     hint = detected_map.permute(2, 0, 1)\n        ...     return hint\n\n\n        >>> depth_estimator = pipeline("depth-estimation")\n\n        >>> pipe_prior = KandinskyV22PriorEmb2EmbPipeline.from_pretrained(\n        ...     "kandinsky-community/kandinsky-2-2-prior", torch_dtype=torch.float16\n        ... )\n        >>> pipe_prior = pipe_prior.to("cuda")\n\n        >>> pipe = KandinskyV22ControlnetImg2ImgPipeline.from_pretrained(\n        ...     "kandinsky-community/kandinsky-2-2-controlnet-depth", torch_dtype=torch.float16\n        ... )\n        >>> pipe = pipe.to("cuda")\n\n        >>> img = load_image(\n        ...     "https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main"\n        ...     "/kandinsky/cat.png"\n        ... ).resize((768, 768))\n\n\n        >>> hint = make_hint(img, depth_estimator).unsqueeze(0).half().to("cuda")\n\n        >>> prompt = "A robot, 4k photo"\n        >>> negative_prior_prompt = "lowres, text, error, cropped, worst quality, low quality, jpeg artifacts, ugly, duplicate, morbid, mutilated, out of frame, extra fingers, mutated hands, poorly drawn hands, poorly drawn face, mutation, deformed, blurry, dehydrated, bad anatomy, bad proportions, extra limbs, cloned face, disfigured, gross proportions, malformed limbs, missing arms, missing legs, extra arms, extra legs, fused fingers, too many fingers, long neck, username, watermark, signature"\n\n        >>> generator = torch.Generator(device="cuda").manual_seed(43)\n\n        >>> img_emb = pipe_prior(prompt=prompt, image=img, strength=0.85, generator=generator)\n        >>> negative_emb = pipe_prior(prompt=negative_prior_prompt, image=img, strength=1, generator=generator)\n\n        >>> images = pipe(\n        ...     image=img,\n        ...     strength=0.5,\n        ...     image_embeds=img_emb.image_embeds,\n        ...     negative_image_embeds=negative_emb.image_embeds,\n        ...     hint=hint,\n        ...     num_inference_steps=50,\n        ...     generator=generator,\n        ...     height=768,\n        ...     width=768,\n        ... ).images\n\n        >>> images[0].save("robot_cat.png")\n        ```\n'





def      __lowercase  (		lowerCamelCase      :  str						,						lowerCamelCase      :  List[str]						,						lowerCamelCase      :  str=8			):
 UpperCamelCase_      :		Union[str, Any]				=      height // scale_factor**2
 if height % scale_factor**2 != 0:
  new_height += 1
 UpperCamelCase_      :		List[str]				=      width // scale_factor**2
 if width % scale_factor**2 != 0:
  new_width += 1
 return new_height * scale_factor, new_width * scale_factor





def      __lowercase  (		lowerCamelCase      :  Optional[Any]						,						lowerCamelCase      :  Optional[int]=512						,						lowerCamelCase      :  str=512			):
 UpperCamelCase_      :		Any				=      pil_image.resize((w, h)						,						resample=Image.BICUBIC						,						reducing_gap=1			)
 UpperCamelCase_      :		Tuple				=      np.array(pil_image.convert('RGB'			)			)
 UpperCamelCase_      :		Optional[int]				=      arr.astype(np.floataa			) / 1_2_7.5 - 1
 UpperCamelCase_      :		int				=      np.transpose(lowerCamelCase						,						[2, 0, 1]			)
 UpperCamelCase_      :		List[Any]				=      torch.from_numpy(lowerCamelCase			).unsqueeze(0			)
 return image






class 	_lowercase		(      snake_case_ ):

 def __init__(				self			:							Union[str, Any]     ,   snake_case			:							UNetaDConditionModel     ,   snake_case			:							DDPMScheduler     ,   snake_case			:							VQModel     ,   )     ->		str:

  """simple docstring"""





  super().__init__()

  self.register_modules(
      unet=snake_case     ,   scheduler=snake_case     ,   movq=snake_case     ,   )
  UpperCamelCase_      :		Optional[Any]				=      2 ** (len(self.movq.config.block_out_channels    ) - 1)

 def 		SCREAMING_SNAKE_CASE__     (				self			:							Dict     ,   snake_case			:							str     ,   snake_case			:							List[Any]     ,   snake_case			:							int    )     ->		str:

  """simple docstring"""





  UpperCamelCase_      :		Any				=      min(int(num_inference_steps * strength    )     ,   snake_case    )

  UpperCamelCase_      :		Optional[Any]				=      max(num_inference_steps - init_timestep     ,   0    )
  UpperCamelCase_      :		Union[str, Any]				=      self.scheduler.timesteps[t_start:]

  return timesteps, num_inference_steps - t_start

 def 		SCREAMING_SNAKE_CASE__     (				self			:							Dict     ,   snake_case			:							int     ,   snake_case			:							Union[str, Any]     ,   snake_case			:							List[str]     ,   snake_case			:							str     ,   snake_case			:							Optional[int]     ,   snake_case			:							Dict     ,   snake_case			:							List[Any]=None    )     ->		Union[str, Any]:

  """simple docstring"""





  if not isinstance(snake_case     ,   (torch.Tensor, PIL.Image.Image, list)    ):
   raise ValueError(
       f"`image` has to be of type `torch.Tensor`, `PIL.Image.Image` or list but is {type(snake_case    )}"    )

  UpperCamelCase_      :		Union[str, Any]				=      image.to(device=snake_case     ,   dtype=snake_case    )

  UpperCamelCase_      :		Any				=      batch_size * num_images_per_prompt

  if image.shape[1] == 4:
   UpperCamelCase_      :		List[Any]				=      image

  else:
   if isinstance(snake_case     ,   snake_case    ) and len(snake_case    ) != batch_size:
    raise ValueError(
        f"You have passed a list of generators of length {len(snake_case    )}, but requested an effective batch"
        f" size of {batch_size}. Make sure the batch size matches the length of the generators."    )

   elif isinstance(snake_case     ,   snake_case    ):
    UpperCamelCase_      :		Any				=      [
        self.movq.encode(image[i : i + 1]    ).latent_dist.sample(generator[i]    ) for i in range(snake_case    )
    ]
    UpperCamelCase_      :		Union[str, Any]				=      torch.cat(snake_case     ,   dim=0    )
   else:
    UpperCamelCase_      :		Optional[Any]				=      self.movq.encode(snake_case    ).latent_dist.sample(snake_case    )

   UpperCamelCase_      :		List[Any]				=      self.movq.config.scaling_factor * init_latents

  UpperCamelCase_      :		List[str]				=      torch.cat([init_latents]     ,   dim=0    )

  UpperCamelCase_      :		Optional[Any]				=      init_latents.shape
  UpperCamelCase_      :		Optional[int]				=      randn_tensor(snake_case     ,   generator=snake_case     ,   device=snake_case     ,   dtype=snake_case    )

  # get latents
  UpperCamelCase_      :		Union[str, Any]				=      self.scheduler.add_noise(snake_case     ,   snake_case     ,   snake_case    )

  UpperCamelCase_      :		Optional[Any]				=      init_latents

  return latents

 def 		SCREAMING_SNAKE_CASE__     (				self			:							List[Any]     ,   snake_case			:							Dict=0    )     ->		Optional[Any]:

  """simple docstring"""





  if is_accelerate_available():
   from accelerate import cpu_offload
  else:
   raise ImportError('Please install accelerate via `pip install accelerate`'    )

  UpperCamelCase_      :		str				=      torch.device(f"cuda:{gpu_id}"    )

  UpperCamelCase_      :		Dict				=      [
      self.unet,
      self.movq,
  ]
  for cpu_offloaded_model in models:
   if cpu_offloaded_model is not None:
    cpu_offload(snake_case     ,   snake_case    )

 def 		SCREAMING_SNAKE_CASE__     (				self			:							str     ,   snake_case			:							Tuple=0    )     ->		Optional[Any]:

  """simple docstring"""





  if is_accelerate_available() and is_accelerate_version('>='     ,   '0.17.0.dev0'    ):
   from accelerate import cpu_offload_with_hook
  else:
   raise ImportError('`enable_model_cpu_offload` requires `accelerate v0.17.0` or higher.'    )

  UpperCamelCase_      :		Any				=      torch.device(f"cuda:{gpu_id}"    )

  if self.device.type != "cpu":
   self.to('cpu'     ,   silence_dtype_warnings=snake_case    )
   torch.cuda.empty_cache()  # otherwise we don't see the memory savings (but they probably exist)

  UpperCamelCase_      :		Any				=      None
  for cpu_offloaded_model in [self.unet, self.movq]:
   UpperCamelCase_,				UpperCamelCase_      :		Any				=      cpu_offload_with_hook(snake_case     ,   snake_case     ,   prev_module_hook=snake_case    )

  # We'll offload the last model manually.
  UpperCamelCase_      :		Optional[int]				=      hook

 @property
 # Copied from diffusers.pipelines.stable_diffusion.pipeline_stable_diffusion.StableDiffusionPipeline._execution_device
 def 		SCREAMING_SNAKE_CASE__     (				self			:							Union[str, Any]    )     ->		Optional[Any]:

  """simple docstring"""





  if not hasattr(self.unet     ,   '_hf_hook'    ):
   return self.device
  for module in self.unet.modules():
   if (
       hasattr(snake_case     ,   '_hf_hook'    )
       and hasattr(module._hf_hook     ,   'execution_device'    )
       and module._hf_hook.execution_device is not None
   ):
    return torch.device(module._hf_hook.execution_device    )
  return self.device


 @torch.no_grad()
 @replace_example_docstring(snake_case    )
 def __call__(				self			:							Optional[int]     ,   snake_case			:							Union[torch.FloatTensor, List[torch.FloatTensor]]     ,   snake_case			:							Union[torch.FloatTensor, PIL.Image.Image, List[torch.FloatTensor], List[PIL.Image.Image]]     ,   snake_case			:							Union[torch.FloatTensor, List[torch.FloatTensor]]     ,   snake_case			:							torch.FloatTensor     ,   snake_case			:							int = 5_1_2     ,   snake_case			:							int = 5_1_2     ,   snake_case			:							int = 1_0_0     ,   snake_case			:							float = 4.0     ,   snake_case			:							float = 0.3     ,   snake_case			:							int = 1     ,   snake_case			:							Optional[Union[torch.Generator, List[torch.Generator]]] = None     ,   snake_case			:							Optional[str] = "pil"     ,   snake_case			:							bool = True     ,   )     ->		Any:

  """simple docstring"""





  UpperCamelCase_      :		List[str]				=      self._execution_device

  UpperCamelCase_      :		str				=      guidance_scale > 1.0

  if isinstance(snake_case     ,   snake_case    ):
   UpperCamelCase_      :		Dict				=      torch.cat(snake_case     ,   dim=0    )
  if isinstance(snake_case     ,   snake_case    ):
   UpperCamelCase_      :		Optional[int]				=      torch.cat(snake_case     ,   dim=0    )
  if isinstance(snake_case     ,   snake_case    ):
   UpperCamelCase_      :		Dict				=      torch.cat(snake_case     ,   dim=0    )

  UpperCamelCase_      :		int				=      image_embeds.shape[0]

  if do_classifier_free_guidance:
   UpperCamelCase_      :		Optional[Any]				=      image_embeds.repeat_interleave(snake_case     ,   dim=0    )
   UpperCamelCase_      :		Any				=      negative_image_embeds.repeat_interleave(snake_case     ,   dim=0    )
   UpperCamelCase_      :		Tuple				=      hint.repeat_interleave(snake_case     ,   dim=0    )

  UpperCamelCase_      :		int				=      torch.cat([negative_image_embeds, image_embeds]     ,   dim=0    ).to(dtype=self.unet.dtype     ,   device=snake_case    )
  UpperCamelCase_      :		Union[str, Any]				=      torch.cat([hint, hint]     ,   dim=0    ).to(dtype=self.unet.dtype     ,   device=snake_case    )

  if not isinstance(snake_case     ,   snake_case    ):
   UpperCamelCase_      :		Optional[Any]				=      [image]
  if not all(isinstance(snake_case     ,   (PIL.Image.Image, torch.Tensor)    ) for i in image    ):
   raise ValueError(
       f"Input is in incorrect format: {[type(snake_case    ) for i in image]}. Currently, we only support  PIL image and pytorch tensor"    )

  UpperCamelCase_      :		Union[str, Any]				=      torch.cat([prepare_image(snake_case     ,   snake_case     ,   snake_case    ) for i in image]     ,   dim=0    )
  UpperCamelCase_      :		Dict				=      image.to(dtype=image_embeds.dtype     ,   device=snake_case    )

  UpperCamelCase_      :		List[Any]				=      self.movq.encode(snake_case    )['latents']
  UpperCamelCase_      :		str				=      latents.repeat_interleave(snake_case     ,   dim=0    )
  self.scheduler.set_timesteps(snake_case     ,   device=snake_case    )
  UpperCamelCase_,				UpperCamelCase_      :		int				=      self.get_timesteps(snake_case     ,   snake_case     ,   snake_case    )
  UpperCamelCase_      :		Any				=      timesteps[:1].repeat(batch_size * num_images_per_prompt    )
  UpperCamelCase_,				UpperCamelCase_      :		Optional[Any]				=      downscale_height_and_width(snake_case     ,   snake_case     ,   self.movq_scale_factor    )
  UpperCamelCase_      :		List[Any]				=      self.prepare_latents(
      snake_case     ,   snake_case     ,   snake_case     ,   snake_case     ,   image_embeds.dtype     ,   snake_case     ,   snake_case    )
  for i, t in enumerate(self.progress_bar(snake_case    )    ):
   # expand the latents if we are doing classifier free guidance
   UpperCamelCase_      :		int				=      torch.cat([latents] * 2    ) if do_classifier_free_guidance else latents

   UpperCamelCase_      :		Optional[Any]				=      {'image_embeds': image_embeds, 'hint': hint}
   UpperCamelCase_      :		Optional[Any]				=      self.unet(
       sample=snake_case     ,   timestep=snake_case     ,   encoder_hidden_states=snake_case     ,   added_cond_kwargs=snake_case     ,   return_dict=snake_case     ,   )[0]

   if do_classifier_free_guidance:
    UpperCamelCase_,				UpperCamelCase_      :		Dict				=      noise_pred.split(latents.shape[1]     ,   dim=1    )
    UpperCamelCase_,				UpperCamelCase_      :		List[Any]				=      noise_pred.chunk(2    )
    UpperCamelCase_,				UpperCamelCase_      :		Union[str, Any]				=      variance_pred.chunk(2    )
    UpperCamelCase_      :		Union[str, Any]				=      noise_pred_uncond + guidance_scale * (noise_pred_text - noise_pred_uncond)
    UpperCamelCase_      :		Tuple				=      torch.cat([noise_pred, variance_pred_text]     ,   dim=1    )

   if not (
       hasattr(self.scheduler.config     ,   'variance_type'    )
       and self.scheduler.config.variance_type in ["learned", "learned_range"]
   ):
    UpperCamelCase_,				UpperCamelCase_      :		int				=      noise_pred.split(latents.shape[1]     ,   dim=1    )

   # compute the previous noisy sample x_t -> x_t-1

   UpperCamelCase_      :		List[Any]				=      self.scheduler.step(
       snake_case     ,   snake_case     ,   snake_case     ,   generator=snake_case     ,   )[0]

  # post-processing
  UpperCamelCase_      :		Any				=      self.movq.decode(snake_case     ,   force_not_quantize=snake_case    )['sample']

  if output_type not in ["pt", "np", "pil"]:
   raise ValueError(f"Only the output types `pt`, `pil` and `np` are supported not output_type={output_type}"    )

  if output_type in ["np", "pil"]:
   UpperCamelCase_      :		List[Any]				=      image * 0.5 + 0.5
   UpperCamelCase_      :		Optional[int]				=      image.clamp(0     ,   1    )
   UpperCamelCase_      :		Dict				=      image.cpu().permute(0     ,   2     ,   3     ,   1    ).float().numpy()

  if output_type == "pil":
   UpperCamelCase_      :		Optional[Any]				=      self.numpy_to_pil(snake_case    )

  if not return_dict:
   return (image,)

  return ImagePipelineOutput(images=snake_case    )



