"""simple docstring"""


def      __UpperCAmelCase       (      lowercase = 10_00		):







  """simple docstring"""
  _UpperCAmelCase    			=   -1
  _UpperCAmelCase    			=   0
  for a in range(1 ,n // 3		):
    # Solving the two equations a**2+b**2=c**2 and a+b+c=N eliminating c
    _UpperCAmelCase    			=   (n * n - 2 * a * n) // (2 * n - 2 * a)
    _UpperCAmelCase    			=   n - a - b
    if c * c == (a * a + b * b):
      _UpperCAmelCase    			=   a * b * c
      if candidate >= product:
        _UpperCAmelCase    			=   candidate
  return product


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






'''simple docstring'''





from typing import List, Optional, Union

import torch
from transformers import (
    XLMRobertaTokenizer,
)

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


UpperCamelCase_		:     List[Any]          =		logging.get_logger(__name__)  # pylint: disable=invalid-name

UpperCamelCase_		:     Dict          =		'''
    Examples:
        ```py
        >>> from diffusers import KandinskyPipeline, KandinskyPriorPipeline
        >>> import torch

        >>> pipe_prior = KandinskyPriorPipeline.from_pretrained("kandinsky-community/Kandinsky-2-1-prior")
        >>> pipe_prior.to("cuda")

        >>> prompt = "red cat, 4k photo"
        >>> out = pipe_prior(prompt)
        >>> image_emb = out.image_embeds
        >>> negative_image_emb = out.negative_image_embeds

        >>> pipe = KandinskyPipeline.from_pretrained("kandinsky-community/kandinsky-2-1")
        >>> pipe.to("cuda")

        >>> image = pipe(
        ...     prompt,
        ...     image_embeds=image_emb,
        ...     negative_image_embeds=negative_image_emb,
        ...     height=768,
        ...     width=768,
        ...     num_inference_steps=100,
        ... ).images

        >>> image[0].save("cat.png")
        ```
'''





def       __a      (  _UpperCamelCase:       Any   ,		_UpperCamelCase:       List[Any]   ,		_UpperCamelCase:       Union[str, Any]=8       )		->					Optional[int]:

     """simple docstring"""




     _snake_case				= h // scale_factor**2
     if h % scale_factor**2 != 0:
          new_h += 1
     _snake_case				= w // scale_factor**2
     if w % scale_factor**2 != 0:
          new_w += 1
     return new_h * scale_factor, new_w * scale_factor





class   _a							(		__lowerCAmelCase				):






     def __init__(					self   ,_SCREAMING_SNAKE_CASE   ,_SCREAMING_SNAKE_CASE   ,_SCREAMING_SNAKE_CASE   ,_SCREAMING_SNAKE_CASE   ,_SCREAMING_SNAKE_CASE   ,)				->     str:
          super().__init__()

          self.register_modules(
              text_encoder=_SCREAMING_SNAKE_CASE   ,tokenizer=_SCREAMING_SNAKE_CASE   ,unet=_SCREAMING_SNAKE_CASE   ,scheduler=_SCREAMING_SNAKE_CASE   ,movq=_SCREAMING_SNAKE_CASE   ,)
          _snake_case				= 2 ** (len(self.movq.config.block_out_channels       ) - 1)






     def 							_lowercase      (					self   ,_SCREAMING_SNAKE_CASE   ,_SCREAMING_SNAKE_CASE   ,_SCREAMING_SNAKE_CASE   ,_SCREAMING_SNAKE_CASE   ,_SCREAMING_SNAKE_CASE   ,_SCREAMING_SNAKE_CASE       )				->     Any:
          if latents is None:
               _snake_case				= randn_tensor(_SCREAMING_SNAKE_CASE   ,generator=_SCREAMING_SNAKE_CASE   ,device=_SCREAMING_SNAKE_CASE   ,dtype=_SCREAMING_SNAKE_CASE       )
          else:
               if latents.shape != shape:
                    raise ValueError(f"""Unexpected latents shape, got {latents.shape}, expected {shape}"""       )
               _snake_case				= latents.to(_SCREAMING_SNAKE_CASE       )

          _snake_case				= latents * scheduler.init_noise_sigma
          return latents






     def 							_lowercase      (					self   ,_SCREAMING_SNAKE_CASE   ,_SCREAMING_SNAKE_CASE   ,_SCREAMING_SNAKE_CASE   ,_SCREAMING_SNAKE_CASE   ,_SCREAMING_SNAKE_CASE=None   ,)				->     Union[str, Any]:
          _snake_case				= len(_SCREAMING_SNAKE_CASE       ) if isinstance(_SCREAMING_SNAKE_CASE   ,_SCREAMING_SNAKE_CASE       ) else 1
          # get prompt text embeddings
          _snake_case				= self.tokenizer(
              _SCREAMING_SNAKE_CASE   ,padding="max_length"   ,truncation=_SCREAMING_SNAKE_CASE   ,max_length=77   ,return_attention_mask=_SCREAMING_SNAKE_CASE   ,add_special_tokens=_SCREAMING_SNAKE_CASE   ,return_tensors="pt"   ,)

          _snake_case				= text_inputs.input_ids
          _snake_case				= self.tokenizer(_SCREAMING_SNAKE_CASE   ,padding="longest"   ,return_tensors="pt"       ).input_ids

          if untruncated_ids.shape[-1] >= text_input_ids.shape[-1] and not torch.equal(_SCREAMING_SNAKE_CASE   ,_SCREAMING_SNAKE_CASE       ):
               _snake_case				= self.tokenizer.batch_decode(untruncated_ids[:, self.tokenizer.model_max_length - 1 : -1]       )
               logger.warning(
                   "The following part of your input was truncated because CLIP can only handle sequences up to"
                   f""" {self.tokenizer.model_max_length} tokens: {removed_text}"""       )

          _snake_case				= text_input_ids.to(_SCREAMING_SNAKE_CASE       )
          _snake_case				= text_inputs.attention_mask.to(_SCREAMING_SNAKE_CASE       )

          _snake_case				,   _snake_case				= self.text_encoder(
              input_ids=_SCREAMING_SNAKE_CASE   ,attention_mask=_SCREAMING_SNAKE_CASE       )

          _snake_case				= prompt_embeds.repeat_interleave(_SCREAMING_SNAKE_CASE   ,dim=0       )
          _snake_case				= text_encoder_hidden_states.repeat_interleave(_SCREAMING_SNAKE_CASE   ,dim=0       )
          _snake_case				= text_mask.repeat_interleave(_SCREAMING_SNAKE_CASE   ,dim=0       )

          if do_classifier_free_guidance:
               _snake_case				= 42
               if negative_prompt is None:
                    _snake_case				= [""] * batch_size
               elif type(_SCREAMING_SNAKE_CASE       ) is not type(_SCREAMING_SNAKE_CASE       ):
                    raise TypeError(
                        f"""`negative_prompt` should be the same type to `prompt`, but got {type(_SCREAMING_SNAKE_CASE       )} !="""
                        f""" {type(_SCREAMING_SNAKE_CASE       )}."""       )
               elif isinstance(_SCREAMING_SNAKE_CASE   ,_SCREAMING_SNAKE_CASE       ):
                    _snake_case				= [negative_prompt]
               elif batch_size != len(_SCREAMING_SNAKE_CASE       ):
                    raise ValueError(
                        f"""`negative_prompt`: {negative_prompt} has batch size {len(_SCREAMING_SNAKE_CASE       )}, but `prompt`:"""
                        f""" {prompt} has batch size {batch_size}. Please make sure that passed `negative_prompt` matches"""
                        " the batch size of `prompt`."       )
               else:
                    _snake_case				= negative_prompt

               _snake_case				= self.tokenizer(
                   _SCREAMING_SNAKE_CASE   ,padding="max_length"   ,max_length=77   ,truncation=_SCREAMING_SNAKE_CASE   ,return_attention_mask=_SCREAMING_SNAKE_CASE   ,add_special_tokens=_SCREAMING_SNAKE_CASE   ,return_tensors="pt"   ,)
               _snake_case				= uncond_input.input_ids.to(_SCREAMING_SNAKE_CASE       )
               _snake_case				= uncond_input.attention_mask.to(_SCREAMING_SNAKE_CASE       )

               _snake_case				,   _snake_case				= self.text_encoder(
                   input_ids=_SCREAMING_SNAKE_CASE   ,attention_mask=_SCREAMING_SNAKE_CASE       )

               # duplicate unconditional embeddings for each generation per prompt, using mps friendly method

               _snake_case				= negative_prompt_embeds.shape[1]
               _snake_case				= negative_prompt_embeds.repeat(1   ,_SCREAMING_SNAKE_CASE       )
               _snake_case				= negative_prompt_embeds.view(batch_size * num_images_per_prompt   ,_SCREAMING_SNAKE_CASE       )

               _snake_case				= uncond_text_encoder_hidden_states.shape[1]
               _snake_case				= uncond_text_encoder_hidden_states.repeat(1   ,_SCREAMING_SNAKE_CASE   ,1       )
               _snake_case				= uncond_text_encoder_hidden_states.view(
                   batch_size * num_images_per_prompt   ,_SCREAMING_SNAKE_CASE   ,-1       )
               _snake_case				= uncond_text_mask.repeat_interleave(_SCREAMING_SNAKE_CASE   ,dim=0       )

               # done duplicates

               # For classifier free guidance, we need to do two forward passes.
               # Here we concatenate the unconditional and text embeddings into a single batch
               # to avoid doing two forward passes
               _snake_case				= torch.cat([negative_prompt_embeds, prompt_embeds]       )
               _snake_case				= torch.cat([uncond_text_encoder_hidden_states, text_encoder_hidden_states]       )

               _snake_case				= torch.cat([uncond_text_mask, text_mask]       )

          return prompt_embeds, text_encoder_hidden_states, text_mask






     def 							_lowercase      (					self   ,_SCREAMING_SNAKE_CASE=0       )				->     List[Any]:
          if is_accelerate_available():
               from accelerate import cpu_offload
          else:
               raise ImportError("Please install accelerate via `pip install accelerate`"       )

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

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






     def 							_lowercase      (					self   ,_SCREAMING_SNAKE_CASE=0       )				->     List[Any]:
          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."       )

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

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

          _snake_case				= None
          for cpu_offloaded_model in [self.text_encoder, self.unet, self.movq]:
               _snake_case				,   _snake_case				= cpu_offload_with_hook(_SCREAMING_SNAKE_CASE   ,_SCREAMING_SNAKE_CASE   ,prev_module_hook=_SCREAMING_SNAKE_CASE       )

          if self.safety_checker is not None:
               _snake_case				,   _snake_case				= cpu_offload_with_hook(self.safety_checker   ,_SCREAMING_SNAKE_CASE   ,prev_module_hook=_SCREAMING_SNAKE_CASE       )

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






     @property
     # Copied from diffusers.pipelines.stable_diffusion.pipeline_stable_diffusion.StableDiffusionPipeline._execution_device
     def 							_lowercase      (					self       )				->     Optional[int]:
          if not hasattr(self.unet   ,"_hf_hook"       ):
               return self.device
          for module in self.unet.modules():
               if (
                   hasattr(_SCREAMING_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(_SCREAMING_SNAKE_CASE       )
     def __call__(					self   ,_SCREAMING_SNAKE_CASE   ,_SCREAMING_SNAKE_CASE   ,_SCREAMING_SNAKE_CASE   ,_SCREAMING_SNAKE_CASE = None   ,_SCREAMING_SNAKE_CASE = 512   ,_SCREAMING_SNAKE_CASE = 512   ,_SCREAMING_SNAKE_CASE = 100   ,_SCREAMING_SNAKE_CASE = 4.0   ,_SCREAMING_SNAKE_CASE = 1   ,_SCREAMING_SNAKE_CASE = None   ,_SCREAMING_SNAKE_CASE = None   ,_SCREAMING_SNAKE_CASE = "pil"   ,_SCREAMING_SNAKE_CASE = True   ,)				->     Union[str, Any]:

          if isinstance(_SCREAMING_SNAKE_CASE   ,_SCREAMING_SNAKE_CASE       ):
               _snake_case				= 1
          elif isinstance(_SCREAMING_SNAKE_CASE   ,_SCREAMING_SNAKE_CASE       ):
               _snake_case				= len(_SCREAMING_SNAKE_CASE       )
          else:
               raise ValueError(f"""`prompt` has to be of type `str` or `list` but is {type(_SCREAMING_SNAKE_CASE       )}"""       )

          _snake_case				= self._execution_device

          _snake_case				= batch_size * num_images_per_prompt
          _snake_case				= guidance_scale > 1.0

          _snake_case				,   _snake_case				,   _snake_case				= self._encode_prompt(
              _SCREAMING_SNAKE_CASE   ,_SCREAMING_SNAKE_CASE   ,_SCREAMING_SNAKE_CASE   ,_SCREAMING_SNAKE_CASE   ,_SCREAMING_SNAKE_CASE       )

          if isinstance(_SCREAMING_SNAKE_CASE   ,_SCREAMING_SNAKE_CASE       ):
               _snake_case				= torch.cat(_SCREAMING_SNAKE_CASE   ,dim=0       )
          if isinstance(_SCREAMING_SNAKE_CASE   ,_SCREAMING_SNAKE_CASE       ):
               _snake_case				= torch.cat(_SCREAMING_SNAKE_CASE   ,dim=0       )

          if do_classifier_free_guidance:
               _snake_case				= image_embeds.repeat_interleave(_SCREAMING_SNAKE_CASE   ,dim=0       )
               _snake_case				= negative_image_embeds.repeat_interleave(_SCREAMING_SNAKE_CASE   ,dim=0       )

          _snake_case				= torch.cat([negative_image_embeds, image_embeds]   ,dim=0       ).to(
              dtype=prompt_embeds.dtype   ,device=_SCREAMING_SNAKE_CASE       )

          self.scheduler.set_timesteps(_SCREAMING_SNAKE_CASE   ,device=_SCREAMING_SNAKE_CASE       )
          _snake_case				= self.scheduler.timesteps

          _snake_case				= self.unet.config.in_channels

          _snake_case				,   _snake_case				= get_new_h_w(_SCREAMING_SNAKE_CASE   ,_SCREAMING_SNAKE_CASE   ,self.movq_scale_factor       )

          # create initial latent
          _snake_case				= self.prepare_latents(
              (batch_size, num_channels_latents, height, width)   ,text_encoder_hidden_states.dtype   ,_SCREAMING_SNAKE_CASE   ,_SCREAMING_SNAKE_CASE   ,_SCREAMING_SNAKE_CASE   ,self.scheduler   ,)

          for i, t in enumerate(self.progress_bar(_SCREAMING_SNAKE_CASE       )       ):
               # expand the latents if we are doing classifier free guidance
               _snake_case				= torch.cat([latents] * 2       ) if do_classifier_free_guidance else latents

               _snake_case				= {"text_embeds": prompt_embeds, "image_embeds": image_embeds}
               _snake_case				= self.unet(
                   sample=_SCREAMING_SNAKE_CASE   ,timestep=_SCREAMING_SNAKE_CASE   ,encoder_hidden_states=_SCREAMING_SNAKE_CASE   ,added_cond_kwargs=_SCREAMING_SNAKE_CASE   ,return_dict=_SCREAMING_SNAKE_CASE   ,)[0]

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

               # compute the previous noisy sample x_t -> x_t-1
               _snake_case				= self.scheduler.step(
                   _SCREAMING_SNAKE_CASE   ,_SCREAMING_SNAKE_CASE   ,_SCREAMING_SNAKE_CASE   ,generator=_SCREAMING_SNAKE_CASE   ,).prev_sample
          # post-processing
          _snake_case				= self.movq.decode(_SCREAMING_SNAKE_CASE   ,force_not_quantize=_SCREAMING_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"]:
               _snake_case				= image * 0.5 + 0.5
               _snake_case				= image.clamp(0   ,1       )
               _snake_case				= image.cpu().permute(0   ,2   ,3   ,1       ).float().numpy()

          if output_type == "pil":
               _snake_case				= self.numpy_to_pil(_SCREAMING_SNAKE_CASE       )

          if not return_dict:
               return (image,)

          return ImagePipelineOutput(images=_SCREAMING_SNAKE_CASE       )


