


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

A :	List[Any]												=     '\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 				UpperCamelCase      (			__magic_name__  :							Dict					,					__magic_name__  :							str					,					__magic_name__  :							Optional[int]=8  )     ->						List[Any]:
		"""simple docstring"""




		lowercase__      =	height // scale_factor**2
		if height % scale_factor**2 != 0:
				new_height += 1
		lowercase__      =	width // scale_factor**2
		if width % scale_factor**2 != 0:
				new_width += 1
		return new_height * scale_factor, new_width * scale_factor






def 				UpperCamelCase      (			__magic_name__  :							Optional[int]					,					__magic_name__  :							str=512					,					__magic_name__  :							List[str]=512  )     ->						Dict:
		"""simple docstring"""




		lowercase__      =	pil_image.resize((w, h)					,					resample=Image.BICUBIC					,					reducing_gap=1  )
		lowercase__      =	np.array(pil_image.convert("""RGB"""  )  )
		lowercase__      =	arr.astype(np.floataa  ) / 1_2_7.5 - 1
		lowercase__      =	np.transpose(__magic_name__					,					[2, 0, 1]  )
		lowercase__      =	torch.from_numpy(__magic_name__  ).unsqueeze(0  )
		return image







class 							A					( UpperCAmelCase__							):
					'''simple docstring'''






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




							"""simple docstring"""


							super().__init__()

							self.register_modules(
							    unet=_UpperCAmelCase   ,      scheduler=_UpperCAmelCase   ,      movq=_UpperCAmelCase   ,      )
							lowercase__      =	2 ** (len(self.movq.config.block_out_channels	) - 1)

					def 						lowerCamelCase__  (self					:		str   ,      _UpperCAmelCase					:		Union[str, Any]   ,      _UpperCAmelCase					:		Dict   ,      _UpperCAmelCase					:		Union[str, Any]	)		->     Union[str, Any]:




							"""simple docstring"""


							lowercase__      =	min(int(num_inference_steps * strength	)   ,      _UpperCAmelCase	)

							lowercase__      =	max(num_inference_steps - init_timestep   ,      0	)
							lowercase__      =	self.scheduler.timesteps[t_start:]

							return timesteps, num_inference_steps - t_start

					def 						lowerCamelCase__  (self					:		Optional[int]   ,      _UpperCAmelCase					:		List[str]   ,      _UpperCAmelCase					:		Tuple   ,      _UpperCAmelCase					:		Optional[Any]   ,      _UpperCAmelCase					:		List[Any]   ,      _UpperCAmelCase					:		int   ,      _UpperCAmelCase					:		List[Any]   ,      _UpperCAmelCase					:		List[Any]=None	)		->     int:




							"""simple docstring"""


							if not isinstance(_UpperCAmelCase   ,      (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(_UpperCAmelCase	)}'''	)

							lowercase__      =	image.to(device=_UpperCAmelCase   ,      dtype=_UpperCAmelCase	)

							lowercase__      =	batch_size * num_images_per_prompt

							if image.shape[1] == 4:
									lowercase__      =	image

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

									elif isinstance(_UpperCAmelCase   ,      _UpperCAmelCase	):
											lowercase__      =	[
											    self.movq.encode(image[i : i + 1]	).latent_dist.sample(generator[i]	) for i in range(_UpperCAmelCase	)
											]
											lowercase__      =	torch.cat(_UpperCAmelCase   ,      dim=0	)
									else:
											lowercase__      =	self.movq.encode(_UpperCAmelCase	).latent_dist.sample(_UpperCAmelCase	)

									lowercase__      =	self.movq.config.scaling_factor * init_latents

							lowercase__      =	torch.cat([init_latents]   ,      dim=0	)

							lowercase__      =	init_latents.shape
							lowercase__      =	randn_tensor(_UpperCAmelCase   ,      generator=_UpperCAmelCase   ,      device=_UpperCAmelCase   ,      dtype=_UpperCAmelCase	)

							# get latents
							lowercase__      =	self.scheduler.add_noise(_UpperCAmelCase   ,      _UpperCAmelCase   ,      _UpperCAmelCase	)

							lowercase__      =	init_latents

							return latents

					def 						lowerCamelCase__  (self					:		Optional[Any]   ,      _UpperCAmelCase					:		List[str]=0	)		->     Dict:




							"""simple docstring"""


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

							lowercase__      =	torch.device(f'''cuda:{gpu_id}'''	)

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

					def 						lowerCamelCase__  (self					:		List[str]   ,      _UpperCAmelCase					:		List[Any]=0	)		->     Optional[int]:




							"""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."""	)

							lowercase__      =	torch.device(f'''cuda:{gpu_id}'''	)

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

							lowercase__      =	None
							for cpu_offloaded_model in [self.unet, self.movq]:
									lowercase__    ,			lowercase__      =	cpu_offload_with_hook(_UpperCAmelCase   ,      _UpperCAmelCase   ,      prev_module_hook=_UpperCAmelCase	)

							# We'll offload the last model manually.
							lowercase__      =	hook

					@property
					# Copied from diffusers.pipelines.stable_diffusion.pipeline_stable_diffusion.StableDiffusionPipeline._execution_device
					def 						lowerCamelCase__  (self					:		str	)		->     Any:




							"""simple docstring"""


							if not hasattr(self.unet   ,      """_hf_hook"""	):
									return self.device
							for module in self.unet.modules():
									if (
									    hasattr(_UpperCAmelCase   ,      """_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(_UpperCAmelCase	)
					def __call__(self					:		Dict   ,      _UpperCAmelCase					:		Union[torch.FloatTensor, List[torch.FloatTensor]]   ,      _UpperCAmelCase					:		Union[torch.FloatTensor, PIL.Image.Image, List[torch.FloatTensor], List[PIL.Image.Image]]   ,      _UpperCAmelCase					:		Union[torch.FloatTensor, List[torch.FloatTensor]]   ,      _UpperCAmelCase					:		torch.FloatTensor   ,      _UpperCAmelCase					:		int = 512   ,      _UpperCAmelCase					:		int = 512   ,      _UpperCAmelCase					:		int = 100   ,      _UpperCAmelCase					:		float = 4.0   ,      _UpperCAmelCase					:		float = 0.3   ,      _UpperCAmelCase					:		int = 1   ,      _UpperCAmelCase					:		Optional[Union[torch.Generator, List[torch.Generator]]] = None   ,      _UpperCAmelCase					:		Optional[str] = "pil"   ,      _UpperCAmelCase					:		bool = True   ,      )		->     int:




							"""simple docstring"""


							lowercase__      =	self._execution_device

							lowercase__      =	guidance_scale > 1.0

							if isinstance(_UpperCAmelCase   ,      _UpperCAmelCase	):
									lowercase__      =	torch.cat(_UpperCAmelCase   ,      dim=0	)
							if isinstance(_UpperCAmelCase   ,      _UpperCAmelCase	):
									lowercase__      =	torch.cat(_UpperCAmelCase   ,      dim=0	)
							if isinstance(_UpperCAmelCase   ,      _UpperCAmelCase	):
									lowercase__      =	torch.cat(_UpperCAmelCase   ,      dim=0	)

							lowercase__      =	image_embeds.shape[0]

							if do_classifier_free_guidance:
									lowercase__      =	image_embeds.repeat_interleave(_UpperCAmelCase   ,      dim=0	)
									lowercase__      =	negative_image_embeds.repeat_interleave(_UpperCAmelCase   ,      dim=0	)
									lowercase__      =	hint.repeat_interleave(_UpperCAmelCase   ,      dim=0	)

							lowercase__      =	torch.cat([negative_image_embeds, image_embeds]   ,      dim=0	).to(dtype=self.unet.dtype   ,      device=_UpperCAmelCase	)
							lowercase__      =	torch.cat([hint, hint]   ,      dim=0	).to(dtype=self.unet.dtype   ,      device=_UpperCAmelCase	)

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

							lowercase__      =	torch.cat([prepare_image(_UpperCAmelCase   ,      _UpperCAmelCase   ,      _UpperCAmelCase	) for i in image]   ,      dim=0	)
							lowercase__      =	image.to(dtype=image_embeds.dtype   ,      device=_UpperCAmelCase	)

							lowercase__      =	self.movq.encode(_UpperCAmelCase	)["""latents"""]
							lowercase__      =	latents.repeat_interleave(_UpperCAmelCase   ,      dim=0	)
							self.scheduler.set_timesteps(_UpperCAmelCase   ,      device=_UpperCAmelCase	)
							lowercase__    ,			lowercase__      =	self.get_timesteps(_UpperCAmelCase   ,      _UpperCAmelCase   ,      _UpperCAmelCase	)
							lowercase__      =	timesteps[:1].repeat(batch_size * num_images_per_prompt	)
							lowercase__    ,			lowercase__      =	downscale_height_and_width(_UpperCAmelCase   ,      _UpperCAmelCase   ,      self.movq_scale_factor	)
							lowercase__      =	self.prepare_latents(
							    _UpperCAmelCase   ,      _UpperCAmelCase   ,      _UpperCAmelCase   ,      _UpperCAmelCase   ,      image_embeds.dtype   ,      _UpperCAmelCase   ,      _UpperCAmelCase	)
							for i, t in enumerate(self.progress_bar(_UpperCAmelCase	)	):
									# expand the latents if we are doing classifier free guidance
									lowercase__      =	torch.cat([latents] * 2	) if do_classifier_free_guidance else latents

									lowercase__      =	{"""image_embeds""": image_embeds, """hint""": hint}
									lowercase__      =	self.unet(
									    sample=_UpperCAmelCase   ,      timestep=_UpperCAmelCase   ,      encoder_hidden_states=_UpperCAmelCase   ,      added_cond_kwargs=_UpperCAmelCase   ,      return_dict=_UpperCAmelCase   ,      )[0]

									if do_classifier_free_guidance:
											lowercase__    ,			lowercase__      =	noise_pred.split(latents.shape[1]   ,      dim=1	)
											lowercase__    ,			lowercase__      =	noise_pred.chunk(2	)
											lowercase__    ,			lowercase__      =	variance_pred.chunk(2	)
											lowercase__      =	noise_pred_uncond + guidance_scale * (noise_pred_text - noise_pred_uncond)
											lowercase__      =	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"]
									):
											lowercase__    ,			lowercase__      =	noise_pred.split(latents.shape[1]   ,      dim=1	)

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

									lowercase__      =	self.scheduler.step(
									    _UpperCAmelCase   ,      _UpperCAmelCase   ,      _UpperCAmelCase   ,      generator=_UpperCAmelCase   ,      )[0]

							# post-processing
							lowercase__      =	self.movq.decode(_UpperCAmelCase   ,      force_not_quantize=_UpperCAmelCase	)["""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"]:
									lowercase__      =	image * 0.5 + 0.5
									lowercase__      =	image.clamp(0   ,      1	)
									lowercase__      =	image.cpu().permute(0   ,      2   ,      3   ,      1	).float().numpy()

							if output_type == "pil":
									lowercase__      =	self.numpy_to_pil(_UpperCAmelCase	)

							if not return_dict:
									return (image,)

							return ImagePipelineOutput(images=_UpperCAmelCase	)





import math






def 				UpperCamelCase      (			__magic_name__  :							int  )     ->						bool:
		"""simple docstring"""




		if 1 < number < 4:
				# 2 and 3 are primes
				return True
		elif number < 2 or number % 2 == 0 or number % 3 == 0:
				# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
				return False

		# All primes number are in format of 6k +/- 1
		for i in range(5					,					int(math.sqrt(__magic_name__  ) + 1  )					,					6  ):
				if number % i == 0 or number % (i + 2) == 0:
						return False
		return True






def 				UpperCamelCase      (			__magic_name__  :							int = 1000					,					__magic_name__  :							int = 1000  )     ->						int:
		"""simple docstring"""




		lowercase__      =	[0, 0, 0]  # length, a, b
		for a in range((a_limit * -1) + 1					,					__magic_name__  ):
				for b in range(2					,					__magic_name__  ):
						if is_prime(__magic_name__  ):
								lowercase__      =	0
								lowercase__      =	0
								while is_prime((n**2) + (a * n) + b  ):
										count += 1
										n += 1
								if count > longest[0]:
										lowercase__      =	[count, a, b]
		lowercase__      =	longest[1] * longest[2]
		return ans


if __name__ == "__main__":
	print(solution(1_0_0_0, 1_0_0_0))

