

from itertools import permutations







def _a				( SCREAMING_SNAKE_CASE	:    List[Any] = 5	)					->					int:

 """simple docstring"""






 if gon_side < 3 or gon_side > 5:
  raise ValueError('gon_side must be in the range [3, 5]'	)

 # Since it's 16, we know 10 is on the outer ring
 # Put the big numbers at the end so that they are never the first number
 __lowerCAmelCase:     str     			=   list(range(gon_side + 1					,      0					,      -1	)	)
 __lowerCAmelCase:     Tuple     			=   list(range(gon_side + 2					,      gon_side * 2 + 1	)	)

 for perm in permutations(small_numbers + big_numbers	):
  __lowerCAmelCase:     str     			=   generate_gon_ring(snake_case_					,      list(snake_case_	)	)
  if is_magic_gon(snake_case_	):
   return int(''.join(str(snake_case_	) for n in numbers	)	)

 __lowerCAmelCase:     Any     			=   f'''Magic {gon_side}-gon ring is impossible'''
 raise ValueError(snake_case_	)







def _a				( SCREAMING_SNAKE_CASE	:    Union[str, Any]					,      SCREAMING_SNAKE_CASE	:    Union[str, Any]	)					->					list[int]:

 """simple docstring"""






 __lowerCAmelCase:     List[Any]     			=   [0] * (gon_side * 3)
 __lowerCAmelCase:     List[Any]     			=   perm[0:3]
 perm.append(perm[1]	)

 __lowerCAmelCase:     Optional[int]     			=   1 if gon_side < 5 else 2

 for i in range(1					,      len(snake_case_	) // 3 + magic_number	):
  __lowerCAmelCase:     Dict     			=   perm[2 * i + 1]
  __lowerCAmelCase:     List[str]     			=   result[3 * i - 1]
  __lowerCAmelCase:     Optional[int]     			=   perm[2 * i + 2]

 return result







def _a				( SCREAMING_SNAKE_CASE	:    List[Any]	)					->					bool:

 """simple docstring"""






 if len(snake_case_	) % 3 != 0:
  raise ValueError('a gon ring should have a length that is a multiple of 3'	)

 if min(numbers[::3]	) != numbers[0]:
  return False

 __lowerCAmelCase:     Optional[int]     			=   sum(numbers[:3]	)

 return all(sum(numbers[i : i + 3]	) == total for i in range(3					,      len(snake_case_	)					,      3	)	)


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








from typing import Union

import torch
from PIL import Image
from torchvision import transforms as tfms
from tqdm.auto import tqdm
from transformers import CLIPTextModel, CLIPTokenizer

from diffusers import (
    AutoencoderKL,
    DDIMScheduler,
    DiffusionPipeline,
    LMSDiscreteScheduler,
    PNDMScheduler,
    UNetaDConditionModel,
)






class 							A_				(	snake_case__      ):


     def __init__(							self    :	List[Any]    ,						UpperCAmelCase    :	AutoencoderKL    ,						UpperCAmelCase    :	CLIPTextModel    ,						UpperCAmelCase    :	CLIPTokenizer    ,						UpperCAmelCase    :	UNetaDConditionModel    ,						UpperCAmelCase    :	Union[PNDMScheduler, LMSDiscreteScheduler, DDIMScheduler]    ,						)							->			Tuple:
      super().__init__()

      self.register_modules(vae=UpperCAmelCase    ,						text_encoder=UpperCAmelCase    ,						tokenizer=UpperCAmelCase    ,						unet=UpperCAmelCase    ,						scheduler=UpperCAmelCase      )


     def 						UpperCAmelCase						(							self    :	str    ,						UpperCAmelCase    :	Dict      )							->			Any:
      with torch.no_grad():
       __lowerCAmelCase:     Tuple     			=   self.vae.encode(tfms.ToTensor()(UpperCAmelCase      ).unsqueeze(0      ).to(self.device      ) * 2 - 1      )
       __lowerCAmelCase:     Tuple     			=   0.18215 * latent.latent_dist.sample()
      return latent


     def 						UpperCAmelCase						(							self    :	List[Any]    ,						UpperCAmelCase    :	str      )							->			int:
      __lowerCAmelCase:     Optional[Any]     			=   (1 / 0.18215) * latent
      with torch.no_grad():
       __lowerCAmelCase:     str     			=   self.vae.decode(UpperCAmelCase      ).sample
      __lowerCAmelCase:     Any     			=   (img / 2 + 0.5).clamp(0    ,						1      )
      __lowerCAmelCase:     Optional[Any]     			=   img.detach().cpu().permute(0    ,						2    ,						3    ,						1      ).numpy()
      __lowerCAmelCase:     List[str]     			=   (img * 2_5_5).round().astype('uint8'      )
      return Image.fromarray(img[0]      )


     def 						UpperCAmelCase						(							self    :	Optional[Any]    ,						UpperCAmelCase    :	Tuple      )							->			str:
      __lowerCAmelCase:     Dict     			=   self.tokenizer(
          UpperCAmelCase    ,						padding='max_length'    ,						max_length=self.tokenizer.model_max_length    ,						truncation=UpperCAmelCase    ,						return_tensors='pt'    ,						)

      __lowerCAmelCase:     Any     			=   self.text_encoder(text_input.input_ids.to(self.device      )      )[0]

      __lowerCAmelCase:     List[str]     			=   self.tokenizer(
          ''    ,						padding='max_length'    ,						max_length=self.tokenizer.model_max_length    ,						truncation=UpperCAmelCase    ,						return_tensors='pt'    ,						)

      __lowerCAmelCase:     str     			=   self.text_encoder(uncond_input.input_ids.to(self.device      )      )[0]

      return torch.cat([uncond_embedding, text_embedding]      )


     def __call__(							self    :	Optional[int]    ,						UpperCAmelCase    :	Image.Image    ,						UpperCAmelCase    :	str    ,						UpperCAmelCase    :	float = 0.3    ,						UpperCAmelCase    :	float = 0.6    ,						UpperCAmelCase    :	float = 0.5    ,						UpperCAmelCase    :	int = 4_2    ,						UpperCAmelCase    :	int = 5_0    ,						UpperCAmelCase    :	float = 7.5    ,						)							->			Image.Image:
      __lowerCAmelCase:     Optional[int]     			=   steps - int(kmin * steps      )
      __lowerCAmelCase:     Dict     			=   steps - int(kmax * steps      )

      __lowerCAmelCase:     Union[str, Any]     			=   self.prep_text(UpperCAmelCase      )

      self.scheduler.set_timesteps(UpperCAmelCase      )

      __lowerCAmelCase			,							__lowerCAmelCase:     str     			=   img.size
      __lowerCAmelCase:     List[Any]     			=   self.encode(UpperCAmelCase      )

      torch.manual_seed(UpperCAmelCase      )
      __lowerCAmelCase:     Optional[int]     			=   torch.randn(
          (1, self.unet.config.in_channels, height // 8, width // 8)    ,						).to(self.device      )

      __lowerCAmelCase:     int     			=   self.scheduler.add_noise(
          UpperCAmelCase    ,						UpperCAmelCase    ,						timesteps=self.scheduler.timesteps[tmax]    ,						)

      __lowerCAmelCase:     Tuple     			=   torch.cat([latents] * 2      )

      __lowerCAmelCase:     int     			=   self.scheduler.scale_model_input(UpperCAmelCase    ,						self.scheduler.timesteps[tmax]      )

      with torch.no_grad():
       __lowerCAmelCase:     List[str]     			=   self.unet(
           UpperCAmelCase    ,						self.scheduler.timesteps[tmax]    ,						encoder_hidden_states=UpperCAmelCase    ,						).sample

      __lowerCAmelCase			,							__lowerCAmelCase:     Optional[Any]     			=   pred.chunk(2      )
      __lowerCAmelCase:     Union[str, Any]     			=   pred_uncond + guidance_scale * (pred_text - pred_uncond)

      __lowerCAmelCase:     List[str]     			=   self.scheduler.step(UpperCAmelCase    ,						self.scheduler.timesteps[tmax]    ,						UpperCAmelCase      ).prev_sample

      for i, t in enumerate(tqdm(self.scheduler.timesteps      )      ):
       if i > tmax:
        if i < tmin:  # layout generation phase
         __lowerCAmelCase:     Optional[Any]     			=   self.scheduler.add_noise(
             UpperCAmelCase    ,						UpperCAmelCase    ,						timesteps=UpperCAmelCase    ,						)

         __lowerCAmelCase:     List[Any]     			=   (mix_factor * latents) + (
             1 - mix_factor
         ) * orig_latents  # interpolating between layout noise and conditionally generated noise to preserve layout sematics
         __lowerCAmelCase:     Optional[Any]     			=   torch.cat([input] * 2      )

        else:  # content generation phase
         __lowerCAmelCase:     str     			=   torch.cat([latents] * 2      )

        __lowerCAmelCase:     List[Any]     			=   self.scheduler.scale_model_input(UpperCAmelCase    ,						UpperCAmelCase      )

        with torch.no_grad():
         __lowerCAmelCase:     Any     			=   self.unet(
             UpperCAmelCase    ,						UpperCAmelCase    ,						encoder_hidden_states=UpperCAmelCase    ,						).sample

        __lowerCAmelCase			,							__lowerCAmelCase:     Optional[int]     			=   pred.chunk(2      )
        __lowerCAmelCase:     Union[str, Any]     			=   pred_uncond + guidance_scale * (pred_text - pred_uncond)

        __lowerCAmelCase:     List[str]     			=   self.scheduler.step(UpperCAmelCase    ,						UpperCAmelCase    ,						UpperCAmelCase      ).prev_sample

      return self.decode(UpperCAmelCase      )





