


from itertools import permutations

def       _a	(					SCREAMING_SNAKE_CASE						:					int = 5  ):







 """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
 UpperCamelCase__       :     str 							= list(range(gon_side + 1     ,			0     ,			-1  )  )
 UpperCamelCase__       :     Optional[Any] 							= list(range(gon_side + 2     ,			gon_side * 2 + 1  )  )

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

 UpperCamelCase__       :     int 							= F"Magic {gon_side}-gon ring is impossible"
 raise ValueError(SCREAMING_SNAKE_CASE  )

def       _a	(					SCREAMING_SNAKE_CASE						:					int     ,			SCREAMING_SNAKE_CASE						:					list[int]  ):







 """simple docstring"""



 UpperCamelCase__       :     Optional[Any] 							= [0] * (gon_side * 3)
 UpperCamelCase__       :     int 							= perm[0:3]
 perm.append(perm[1]  )

 UpperCamelCase__       :     Union[str, Any] 							= 1 if gon_side < 5 else 2

 for i in range(1     ,			len(SCREAMING_SNAKE_CASE  ) // 3 + magic_number  ):
  UpperCamelCase__       :     int 							= perm[2 * i + 1]
  UpperCamelCase__       :     str 							= result[3 * i - 1]
  UpperCamelCase__       :     Any 							= perm[2 * i + 2]

 return result

def       _a	(					SCREAMING_SNAKE_CASE						:					list[int]  ):







 """simple docstring"""



 if len(SCREAMING_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

 UpperCamelCase__       :     List[Any] 							= sum(numbers[:3]  )

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


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






from typing import Any, Callable, Dict, List, Optional, Union

import PIL.Image
import torch
from transformers import CLIPImageProcessor, CLIPTextModel, CLIPTokenizer

from diffusers import (
    AutoencoderKL,
    DDIMScheduler,
    DiffusionPipeline,
    LMSDiscreteScheduler,
    PNDMScheduler,
    StableDiffusionImgaImgPipeline,
    StableDiffusionInpaintPipelineLegacy,
    StableDiffusionPipeline,
    UNetaDConditionModel,
)
from diffusers.configuration_utils import FrozenDict
from diffusers.pipelines.stable_diffusion.safety_checker import StableDiffusionSafetyChecker
from diffusers.utils import deprecate, logging


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

class    __magic_name__						(  __lowerCAmelCase):
     A:		Dict								=   ["safety_checker", "feature_extractor"]


     def __init__(   self				:  List[str]				,						lowerCamelCase__				:  AutoencoderKL				,						lowerCamelCase__				:  CLIPTextModel				,						lowerCamelCase__				:  CLIPTokenizer				,						lowerCamelCase__				:  UNetaDConditionModel				,						lowerCamelCase__				:  Union[DDIMScheduler, PNDMScheduler, LMSDiscreteScheduler]				,						lowerCamelCase__				:  StableDiffusionSafetyChecker				,						lowerCamelCase__				:  CLIPImageProcessor				,						lowerCamelCase__				:  bool = True				,						)	->   Optional[Any]:





      '''simple docstring'''






      super().__init__()
      if hasattr(scheduler.config				,						'''steps_offset'''      ) and scheduler.config.steps_offset != 1:
       UpperCamelCase__       :     int 							= (
           F"The configuration file of this scheduler: {scheduler} is outdated. `steps_offset`"
           F" should be set to 1 instead of {scheduler.config.steps_offset}. Please make sure "
           '''to update the config accordingly as leaving `steps_offset` might led to incorrect results'''
           ''' in future versions. If you have downloaded this checkpoint from the Hugging Face Hub,'''
           ''' it would be very nice if you could open a Pull request for the `scheduler/scheduler_config.json`'''
           ''' file'''
       )
       deprecate('''steps_offset!=1'''				,						'''1.0.0'''				,						lowerCamelCase__				,						standard_warn=lowerCamelCase__      )
       UpperCamelCase__       :     int 							= dict(scheduler.config      )
       UpperCamelCase__       :     List[str] 							= 1
       UpperCamelCase__       :     List[str] 							= FrozenDict(lowerCamelCase__      )

      self.register_modules(
          vae=lowerCamelCase__				,						text_encoder=lowerCamelCase__				,						tokenizer=lowerCamelCase__				,						unet=lowerCamelCase__				,						scheduler=lowerCamelCase__				,						safety_checker=lowerCamelCase__				,						feature_extractor=lowerCamelCase__				,						)
      self.register_to_config(requires_safety_checker=lowerCamelCase__      )


     @property
     def   UpperCAmelCase__						(   self				:  str      )	->   Dict[str, Any]:





      '''simple docstring'''






      return {k: getattr(self				,						lowerCamelCase__      ) for k in self.config.keys() if not k.startswith('''_'''      )}


     def   UpperCAmelCase__						(   self				:  str				,						lowerCamelCase__				:  Optional[Union[str, int]] = "auto"      )	->   str:





      '''simple docstring'''






      if slice_size == "auto":
       # half the attention head size is usually a good trade-off between
       # speed and memory
       UpperCamelCase__       :     Dict 							= self.unet.config.attention_head_dim // 2
      self.unet.set_attention_slice(lowerCamelCase__      )


     def   UpperCAmelCase__						(   self				:  int      )	->   Tuple:





      '''simple docstring'''






      self.enable_attention_slicing(lowerCamelCase__      )


     @torch.no_grad()
     def   UpperCAmelCase__						(   self				:  Optional[Any]				,						lowerCamelCase__				:  Union[str, List[str]]				,						lowerCamelCase__				:  Union[torch.FloatTensor, PIL.Image.Image]				,						lowerCamelCase__				:  Union[torch.FloatTensor, PIL.Image.Image]				,						lowerCamelCase__				:  float = 0.8				,						lowerCamelCase__				:  Optional[int] = 50				,						lowerCamelCase__				:  Optional[float] = 7.5				,						lowerCamelCase__				:  Optional[Union[str, List[str]]] = None				,						lowerCamelCase__				:  Optional[int] = 1				,						lowerCamelCase__				:  Optional[float] = 0.0				,						lowerCamelCase__				:  Optional[torch.Generator] = None				,						lowerCamelCase__				:  Optional[str] = "pil"				,						lowerCamelCase__				:  bool = True				,						lowerCamelCase__				:  Optional[Callable[[int, int, torch.FloatTensor], None]] = None				,						lowerCamelCase__				:  int = 1				,						)	->   Optional[Any]:





      '''simple docstring'''






      return StableDiffusionInpaintPipelineLegacy(**self.components      )(
          prompt=lowerCamelCase__				,						image=lowerCamelCase__				,						mask_image=lowerCamelCase__				,						strength=lowerCamelCase__				,						num_inference_steps=lowerCamelCase__				,						guidance_scale=lowerCamelCase__				,						negative_prompt=lowerCamelCase__				,						num_images_per_prompt=lowerCamelCase__				,						eta=lowerCamelCase__				,						generator=lowerCamelCase__				,						output_type=lowerCamelCase__				,						return_dict=lowerCamelCase__				,						callback=lowerCamelCase__				,						)


     @torch.no_grad()
     def   UpperCAmelCase__						(   self				:  Any				,						lowerCamelCase__				:  Union[str, List[str]]				,						lowerCamelCase__				:  Union[torch.FloatTensor, PIL.Image.Image]				,						lowerCamelCase__				:  float = 0.8				,						lowerCamelCase__				:  Optional[int] = 50				,						lowerCamelCase__				:  Optional[float] = 7.5				,						lowerCamelCase__				:  Optional[Union[str, List[str]]] = None				,						lowerCamelCase__				:  Optional[int] = 1				,						lowerCamelCase__				:  Optional[float] = 0.0				,						lowerCamelCase__				:  Optional[torch.Generator] = None				,						lowerCamelCase__				:  Optional[str] = "pil"				,						lowerCamelCase__				:  bool = True				,						lowerCamelCase__				:  Optional[Callable[[int, int, torch.FloatTensor], None]] = None				,						lowerCamelCase__				:  int = 1				,						**lowerCamelCase__				:  str				,						)	->   str:





      '''simple docstring'''






      return StableDiffusionImgaImgPipeline(**self.components      )(
          prompt=lowerCamelCase__				,						image=lowerCamelCase__				,						strength=lowerCamelCase__				,						num_inference_steps=lowerCamelCase__				,						guidance_scale=lowerCamelCase__				,						negative_prompt=lowerCamelCase__				,						num_images_per_prompt=lowerCamelCase__				,						eta=lowerCamelCase__				,						generator=lowerCamelCase__				,						output_type=lowerCamelCase__				,						return_dict=lowerCamelCase__				,						callback=lowerCamelCase__				,						callback_steps=lowerCamelCase__				,						)


     @torch.no_grad()
     def   UpperCAmelCase__						(   self				:  Optional[int]				,						lowerCamelCase__				:  Union[str, List[str]]				,						lowerCamelCase__				:  int = 512				,						lowerCamelCase__				:  int = 512				,						lowerCamelCase__				:  int = 50				,						lowerCamelCase__				:  float = 7.5				,						lowerCamelCase__				:  Optional[Union[str, List[str]]] = None				,						lowerCamelCase__				:  Optional[int] = 1				,						lowerCamelCase__				:  float = 0.0				,						lowerCamelCase__				:  Optional[torch.Generator] = None				,						lowerCamelCase__				:  Optional[torch.FloatTensor] = None				,						lowerCamelCase__				:  Optional[str] = "pil"				,						lowerCamelCase__				:  bool = True				,						lowerCamelCase__				:  Optional[Callable[[int, int, torch.FloatTensor], None]] = None				,						lowerCamelCase__				:  int = 1				,						)	->   Optional[Any]:





      '''simple docstring'''






      return StableDiffusionPipeline(**self.components      )(
          prompt=lowerCamelCase__				,						height=lowerCamelCase__				,						width=lowerCamelCase__				,						num_inference_steps=lowerCamelCase__				,						guidance_scale=lowerCamelCase__				,						negative_prompt=lowerCamelCase__				,						num_images_per_prompt=lowerCamelCase__				,						eta=lowerCamelCase__				,						generator=lowerCamelCase__				,						latents=lowerCamelCase__				,						output_type=lowerCamelCase__				,						return_dict=lowerCamelCase__				,						callback=lowerCamelCase__				,						callback_steps=lowerCamelCase__				,						)


