code: 
  
  
  
  
  
  
  """simple docstring"""
  
  from itertools import permutations
  
  def 	__lowerCamelCase			(						__UpperCamelCase = 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_     :							Union[str, Any]             =    list(range(gon_side + 1   , 0   , -1 ) )
  		lowerCAmelCase_     :							str             =    list(range(gon_side + 2   , gon_side * 2 + 1 ) )
  
  		for perm in permutations(small_numbers + big_numbers ):
  				lowerCAmelCase_     :							Optional[Any]             =    generate_gon_ring(_UpperCAmelCase   , list(_UpperCAmelCase ) )
  				if is_magic_gon(_UpperCAmelCase ):
  						return int("".join(str(_UpperCAmelCase ) for n in numbers ) )
  
  		lowerCAmelCase_     :							List[str]             =    f'''Magic {gon_side}-gon ring is impossible'''
  		raise ValueError(_UpperCAmelCase )
  
  def 	__lowerCamelCase			(						__UpperCamelCase   , __UpperCamelCase )		->					list[int]:
  
  		"""simple docstring"""
  
  
  
  
  
  
  
  		lowerCAmelCase_     :							List[str]             =    [0] * (gon_side * 3)
  		lowerCAmelCase_     :							Optional[int]             =    perm[0:3]
  		perm.append(perm[1] )
  
  		lowerCAmelCase_     :							Tuple             =    1 if gon_side < 5 else 2
  
  		for i in range(1   , len(_UpperCAmelCase ) // 3 + magic_number ):
  				lowerCAmelCase_     :							List[str]             =    perm[2 * i + 1]
  				lowerCAmelCase_     :							Optional[int]             =    result[3 * i - 1]
  				lowerCAmelCase_     :							Union[str, Any]             =    perm[2 * i + 2]
  
  		return result
  
  def 	__lowerCamelCase			(						__UpperCamelCase )		->					bool:
  
  		"""simple docstring"""
  
  
  
  
  
  
  
  		if len(_UpperCAmelCase ) % 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_     :							List[str]             =    sum(numbers[:3] )
  
  		return all(sum(numbers[i : i + 3] ) == total for i in range(3   , len(_UpperCAmelCase )   , 3 ) )
  
  
  if __name__ == "__main__":
  					print(solution())
  
  
  
  
  
  
  
style_context: 
  
  
  
  
  
  
  """simple docstring"""
  
  import gc
  import random
  import unittest
  
  import numpy as np
  import torch
  from PIL import Image
  from transformers import CLIPImageProcessor, CLIPVisionConfig, CLIPVisionModelWithProjection
  
  from diffusers import (
      AutoencoderKL,
      DPMSolverMultistepScheduler,
      PNDMScheduler,
      StableDiffusionImageVariationPipeline,
      UNetaDConditionModel,
  )
  from diffusers.utils import floats_tensor, load_image, load_numpy, nightly, slow, torch_device
  from diffusers.utils.testing_utils import enable_full_determinism, require_torch_gpu
  
  from ..pipeline_params import IMAGE_VARIATION_BATCH_PARAMS, IMAGE_VARIATION_PARAMS
  from ..test_pipelines_common import PipelineKarrasSchedulerTesterMixin, PipelineLatentTesterMixin, PipelineTesterMixin
  
  
  enable_full_determinism()
  
  
  class 	__lowerCamelCase       (				A__				,							A__				,							A__				,							unittest.TestCase    ):
  
  
  
  
  
  		'''simple docstring'''
  
  
  
  
  
  
  		a_			:       Union[str, Any]      =							StableDiffusionImageVariationPipeline
  		a_			:       Tuple      =							IMAGE_VARIATION_PARAMS
  		a_			:       Optional[Any]      =							IMAGE_VARIATION_BATCH_PARAMS
  		a_			:       int      =							frozenset([]    )
  		# TO-DO: update image_params once pipeline is refactored with VaeImageProcessor.preprocess
  		a_			:       Optional[int]      =							frozenset([]    )
  
  
  
  
  
  		def      lowerCamelCase (     self							:			Tuple			):
  				torch.manual_seed(0			)
  				lowerCAmelCase_     :							List[Any]             =    UNetaDConditionModel(
  				    block_out_channels=(32, 64)		,    layers_per_block=2		,    sample_size=32		,    in_channels=4		,    out_channels=4		,    down_block_types=("DownBlock2D", "CrossAttnDownBlock2D")		,    up_block_types=("CrossAttnUpBlock2D", "UpBlock2D")		,    cross_attention_dim=32		,    )
  				lowerCAmelCase_     :							int             =    PNDMScheduler(skip_prk_steps=a_			)
  				torch.manual_seed(0			)
  				lowerCAmelCase_     :							List[Any]             =    AutoencoderKL(
  				    block_out_channels=[32, 64]		,    in_channels=3		,    out_channels=3		,    down_block_types=["DownEncoderBlock2D", "DownEncoderBlock2D"]		,    up_block_types=["UpDecoderBlock2D", "UpDecoderBlock2D"]		,    latent_channels=4		,    )
  				torch.manual_seed(0			)
  				lowerCAmelCase_     :							Dict             =    CLIPVisionConfig(
  				    hidden_size=32		,    projection_dim=32		,    intermediate_size=37		,    layer_norm_eps=1e-0_5		,    num_attention_heads=4		,    num_hidden_layers=5		,    image_size=32		,    patch_size=4		,    )
  				lowerCAmelCase_     :							List[Any]             =    CLIPVisionModelWithProjection(a_			)
  				lowerCAmelCase_     :							Union[str, Any]             =    CLIPImageProcessor(crop_size=32		,    size=32			)
  
  				lowerCAmelCase_     :							List[Any]             =    {
  				    "unet": unet,
  				    "scheduler": scheduler,
  				    "vae": vae,
  				    "image_encoder": image_encoder,
  				    "feature_extractor": feature_extractor,
  				    "safety_checker": None,
  				}
  				return components
  
  
  
  
  
  		def      lowerCamelCase (     self							:			Optional[int]		,    a_							:			Tuple		,    a_							:			str=0			):
  				lowerCAmelCase_     :							List[Any]             =    floats_tensor((1, 3, 32, 32)		,    rng=random.Random(a_			)			)
  				lowerCAmelCase_     :							int             =    image.cpu().permute(0		,    2		,    3		,    1			)[0]
  				lowerCAmelCase_     :							List[str]             =    Image.fromarray(np.uinta(a_			)			).convert("RGB"			).resize((32, 32)			)
  				if str(a_			).startswith("mps"			):
  						lowerCAmelCase_     :							Optional[int]             =    torch.manual_seed(a_			)
  				else:
  						lowerCAmelCase_     :							Optional[Any]             =    torch.Generator(device=a_			).manual_seed(a_			)
  				lowerCAmelCase_     :							str             =    {
  				    "image": image,
  				    "generator": generator,
  				    "num_inference_steps": 2,
  				    "guidance_scale": 6.0,
  				    "output_type": "numpy",
  				}
  				return inputs
  
  
  
  
  
  		def      lowerCamelCase (     self							:			Any			):
  				lowerCAmelCase_     :							int             =    "cpu"  # ensure determinism for the device-dependent torch.Generator
  				lowerCAmelCase_     :							Dict             =    self.get_dummy_components()
  				lowerCAmelCase_     :							Union[str, Any]             =    StableDiffusionImageVariationPipeline(**a_			)
  				lowerCAmelCase_     :							int             =    sd_pipe.to(a_			)
  				sd_pipe.set_progress_bar_config(disable=a_			)
  
  				lowerCAmelCase_     :							Tuple             =    self.get_dummy_inputs(a_			)
  				lowerCAmelCase_     :							List[str]             =    sd_pipe(**a_			).images
  				lowerCAmelCase_     :							List[Any]             =    image[0, -3:, -3:, -1]
  
  				assert image.shape == (1, 64, 64, 3)
  				lowerCAmelCase_     :							List[str]             =    np.array([0.5239, 0.5723, 0.4796, 0.5049, 0.5550, 0.4685, 0.5329, 0.4891, 0.4921]			)
  
  				assert np.abs(image_slice.flatten() - expected_slice			).max() < 1e-3
  
  
  
  
  
  		def      lowerCamelCase (     self							:			Union[str, Any]			):
  				lowerCAmelCase_     :							int             =    "cpu"  # ensure determinism for the device-dependent torch.Generator
  				lowerCAmelCase_     :							Optional[Any]             =    self.get_dummy_components()
  				lowerCAmelCase_     :							Tuple             =    StableDiffusionImageVariationPipeline(**a_			)
  				lowerCAmelCase_     :							List[str]             =    sd_pipe.to(a_			)
  				sd_pipe.set_progress_bar_config(disable=a_			)
  
  				lowerCAmelCase_     :							List[str]             =    self.get_dummy_inputs(a_			)
  				lowerCAmelCase_     :							Optional[Any]             =    2 * [inputs["image"]]
  				lowerCAmelCase_     :							Optional[Any]             =    sd_pipe(**a_			)
  
  				lowerCAmelCase_     :							Union[str, Any]             =    output.images
  
  				lowerCAmelCase_     :							Optional[Any]             =    image[-1, -3:, -3:, -1]
  
  				assert image.shape == (2, 64, 64, 3)
  				lowerCAmelCase_     :							int             =    np.array([0.6892, 0.5637, 0.5836, 0.5771, 0.6254, 0.6409, 0.5580, 0.5569, 0.5289]			)
  
  				assert np.abs(image_slice.flatten() - expected_slice			).max() < 1e-3
  
  
  
  
  
  		def      lowerCamelCase (     self							:			str			):
  				super().test_inference_batch_single_identical(expected_max_diff=3e-3			)
  
  
  
  
  
  
  
  @slow
  @require_torch_gpu
  class 	__lowerCamelCase       (				unittest.TestCase    ):
  
  
  
  
  
  		'''simple docstring'''
  
  
  
  
  
  
  		def      lowerCamelCase (     self							:			int			):
  				super().tearDown()
  				gc.collect()
  				torch.cuda.empty_cache()
  
  
  
  
  
  		def      lowerCamelCase (     self							:			Optional[Any]		,    a_							:			Optional[Any]		,    a_							:			List[str]="cpu"		,    a_							:			Optional[Any]=torch.floataa		,    a_							:			Optional[int]=0			):
  				lowerCAmelCase_     :							str             =    torch.Generator(device=a_			).manual_seed(a_			)
  				lowerCAmelCase_     :							str             =    load_image(
  				    "https://huggingface.co/datasets/diffusers/test-arrays/resolve/main"
  				    "/stable_diffusion_imgvar/input_image_vermeer.png"			)
  				lowerCAmelCase_     :							Optional[Any]             =    np.random.RandomState(a_			).standard_normal((1, 4, 64, 64)			)
  				lowerCAmelCase_     :							List[Any]             =    torch.from_numpy(a_			).to(device=a_		,    dtype=a_			)
  				lowerCAmelCase_     :							Any             =    {
  				    "image": init_image,
  				    "latents": latents,
  				    "generator": generator,
  				    "num_inference_steps": 3,
  				    "guidance_scale": 7.5,
  				    "output_type": "numpy",
  				}
  				return inputs
  
  
  
  
  
  		def      lowerCamelCase (     self							:			Any			):
  				lowerCAmelCase_     :							Tuple             =    StableDiffusionImageVariationPipeline.from_pretrained(
  				    "lambdalabs/sd-image-variations-diffusers"		,    safety_checker=a_			)
  				lowerCAmelCase_     :							int             =    sd_pipe.to(a_			)
  				sd_pipe.set_progress_bar_config(disable=a_			)
  
  				lowerCAmelCase_     :							Union[str, Any]             =    self.get_inputs(a_			)
  				lowerCAmelCase_     :							Union[str, Any]             =    sd_pipe(**a_			).images
  				lowerCAmelCase_     :							Optional[int]             =    image[0, -3:, -3:, -1].flatten()
  
  				assert image.shape == (1, 5_12, 5_12, 3)
  				lowerCAmelCase_     :							Optional[Any]             =    np.array([0.84491, 0.90789, 0.75708, 0.78734, 0.83485, 0.70099, 0.66938, 0.68727, 0.61379]			)
  				assert np.abs(image_slice - expected_slice			).max() < 6e-3
  
  
  
  
  
  		def      lowerCamelCase (     self							:			Dict			):
  				lowerCAmelCase_     :							List[str]             =    0
  
  				def callback_fn(a_							:			int		,    a_							:			int		,    a_							:			torch.FloatTensor			) -> None:
  						lowerCAmelCase_     :							str             =    True
  						nonlocal number_of_steps
  						number_of_steps += 1
  						if step == 1:
  								lowerCAmelCase_     :							str             =    latents.detach().cpu().numpy()
  								assert latents.shape == (1, 4, 64, 64)
  								lowerCAmelCase_     :							Dict             =    latents[0, -3:, -3:, -1]
  								lowerCAmelCase_     :							List[Any]             =    np.array(
  								    [-0.1621, 0.2837, -0.7979, -0.1221, -1.3057, 0.7681, -2.1191, 0.0464, 1.6309]			)
  
  								assert np.abs(latents_slice.flatten() - expected_slice			).max() < 5e-2
  						elif step == 2:
  								lowerCAmelCase_     :							Dict             =    latents.detach().cpu().numpy()
  								assert latents.shape == (1, 4, 64, 64)
  								lowerCAmelCase_     :							Tuple             =    latents[0, -3:, -3:, -1]
  								lowerCAmelCase_     :							Dict             =    np.array([0.6299, 1.7500, 1.1992, -2.1582, -1.8994, 0.7334, -0.7090, 1.0137, 1.5273]			)
  
  								assert np.abs(latents_slice.flatten() - expected_slice			).max() < 5e-2
  
  				lowerCAmelCase_     :							Union[str, Any]             =    False
  
  				lowerCAmelCase_     :							str             =    StableDiffusionImageVariationPipeline.from_pretrained(
  				    "fusing/sd-image-variations-diffusers"		,    safety_checker=a_		,    torch_dtype=torch.floataa		,    )
  				pipe.to(a_			)
  				pipe.set_progress_bar_config(disable=a_			)
  				pipe.enable_attention_slicing()
  
  				lowerCAmelCase_     :							Tuple             =    self.get_inputs(a_		,    dtype=torch.floataa			)
  				pipe(**a_		,    callback=a_		,    callback_steps=1			)
  				assert callback_fn.has_been_called
  				assert number_of_steps == inputs["num_inference_steps"]
  
  
  
  
  
  		def      lowerCamelCase (     self							:			Optional[Any]			):
  				torch.cuda.empty_cache()
  				torch.cuda.reset_max_memory_allocated()
  				torch.cuda.reset_peak_memory_stats()
  
  				lowerCAmelCase_     :							Tuple             =    "fusing/sd-image-variations-diffusers"
  				lowerCAmelCase_     :							str             =    StableDiffusionImageVariationPipeline.from_pretrained(
  				    a_		,    safety_checker=a_		,    torch_dtype=torch.floataa			)
  				lowerCAmelCase_     :							int             =    pipe.to(a_			)
  				pipe.set_progress_bar_config(disable=a_			)
  				pipe.enable_attention_slicing(1			)
  				pipe.enable_sequential_cpu_offload()
  
  				lowerCAmelCase_     :							List[str]             =    self.get_inputs(a_		,    dtype=torch.floataa			)
  				lowerCAmelCase_     :							Any             =    pipe(**a_			)
  
  				lowerCAmelCase_     :							List[Any]             =    torch.cuda.max_memory_allocated()
  				# make sure that less than 2.6 GB is allocated
  				assert mem_bytes < 2.6 * 10**9
  
  
  
  
  
  
  
  @nightly
  @require_torch_gpu
  class 	__lowerCamelCase       (				unittest.TestCase    ):
  
  
  
  
  
  		'''simple docstring'''
  
  
  
  
  
  
  		def      lowerCamelCase (     self							:			Tuple			):
  				super().tearDown()
  				gc.collect()
  				torch.cuda.empty_cache()
  
  
  
  
  
  		def      lowerCamelCase (     self							:			Optional[int]		,    a_							:			int		,    a_							:			int="cpu"		,    a_							:			str=torch.floataa		,    a_							:			Optional[Any]=0			):
  				lowerCAmelCase_     :							str             =    torch.Generator(device=a_			).manual_seed(a_			)
  				lowerCAmelCase_     :							int             =    load_image(
  				    "https://huggingface.co/datasets/diffusers/test-arrays/resolve/main"
  				    "/stable_diffusion_imgvar/input_image_vermeer.png"			)
  				lowerCAmelCase_     :							Optional[Any]             =    np.random.RandomState(a_			).standard_normal((1, 4, 64, 64)			)
  				lowerCAmelCase_     :							Optional[int]             =    torch.from_numpy(a_			).to(device=a_		,    dtype=a_			)
  				lowerCAmelCase_     :							Union[str, Any]             =    {
  				    "image": init_image,
  				    "latents": latents,
  				    "generator": generator,
  				    "num_inference_steps": 50,
  				    "guidance_scale": 7.5,
  				    "output_type": "numpy",
  				}
  				return inputs
  
  
  
  
  
  		def      lowerCamelCase (     self							:			Optional[int]			):
  				lowerCAmelCase_     :							Any             =    StableDiffusionImageVariationPipeline.from_pretrained("fusing/sd-image-variations-diffusers"			)
  				sd_pipe.to(a_			)
  				sd_pipe.set_progress_bar_config(disable=a_			)
  
  				lowerCAmelCase_     :							List[str]             =    self.get_inputs(a_			)
  				lowerCAmelCase_     :							int             =    sd_pipe(**a_			).images[0]
  
  				lowerCAmelCase_     :							Optional[Any]             =    load_numpy(
  				    "https://huggingface.co/datasets/diffusers/test-arrays/resolve/main"
  				    "/stable_diffusion_imgvar/lambdalabs_variations_pndm.npy"			)
  				lowerCAmelCase_     :							List[Any]             =    np.abs(expected_image - image			).max()
  				assert max_diff < 1e-3
  
  
  
  
  
  		def      lowerCamelCase (     self							:			Any			):
  				lowerCAmelCase_     :							List[Any]             =    StableDiffusionImageVariationPipeline.from_pretrained("fusing/sd-image-variations-diffusers"			)
  				lowerCAmelCase_     :							Tuple             =    DPMSolverMultistepScheduler.from_config(sd_pipe.scheduler.config			)
  				sd_pipe.to(a_			)
  				sd_pipe.set_progress_bar_config(disable=a_			)
  
  				lowerCAmelCase_     :							Optional[int]             =    self.get_inputs(a_			)
  				lowerCAmelCase_     :							Tuple             =    25
  				lowerCAmelCase_     :							int             =    sd_pipe(**a_			).images[0]
  
  				lowerCAmelCase_     :							Union[str, Any]             =    load_numpy(
  				    "https://huggingface.co/datasets/diffusers/test-arrays/resolve/main"
  				    "/stable_diffusion_imgvar/lambdalabs_variations_dpm_multi.npy"			)
  				lowerCAmelCase_     :							Optional[Any]             =    np.abs(expected_image - image			).max()
  				assert max_diff < 1e-3
  