




from itertools import permutations



def 							_A   (						lowerCAmelCase_     :					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
     lowerCAmelCase__		= list(range(gon_side + 1   ,				0   ,				-1			)			)
     lowerCAmelCase__		= list(range(gon_side + 2   ,				gon_side * 2 + 1			)			)

     for perm in permutations(small_numbers + big_numbers			):
          lowerCAmelCase__		= generate_gon_ring(lowerCAmelCase_   ,				list(lowerCAmelCase_			)			)
          if is_magic_gon(lowerCAmelCase_			):
               return int("".join(str(lowerCAmelCase_			) for n in numbers			)			)

     lowerCAmelCase__		= F'Magic {gon_side}-gon ring is impossible'
     raise ValueError(lowerCAmelCase_			)



def 							_A   (						lowerCAmelCase_     :					int   ,				lowerCAmelCase_     :					list[int]			):
     """simple docstring"""

     lowerCAmelCase__		= [0] * (gon_side * 3)
     lowerCAmelCase__		= perm[0:3]
     perm.append(perm[1]			)

     lowerCAmelCase__		= 1 if gon_side < 5 else 2

     for i in range(1   ,				len(lowerCAmelCase_			) // 3 + magic_number			):
          lowerCAmelCase__		= perm[2 * i + 1]
          lowerCAmelCase__		= result[3 * i - 1]
          lowerCAmelCase__		= perm[2 * i + 2]

     return result



def 							_A   (						lowerCAmelCase_     :					list[int]			):
     """simple docstring"""

     if len(lowerCAmelCase_			) % 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__		= sum(numbers[:3]			)

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


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






from ..utils import (
    OptionalDependencyNotAvailable,
    is_flax_available,
    is_invisible_watermark_available,
    is_k_diffusion_available,
    is_librosa_available,
    is_note_seq_available,
    is_onnx_available,
    is_torch_available,
    is_transformers_available,
)


try:
     if not is_torch_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     from ..utils.dummy_pt_objects import *  # noqa F403
else:
     from .consistency_models import ConsistencyModelPipeline
     from .dance_diffusion import DanceDiffusionPipeline
     from .ddim import DDIMPipeline
     from .ddpm import DDPMPipeline
     from .dit import DiTPipeline
     from .latent_diffusion import LDMSuperResolutionPipeline
     from .latent_diffusion_uncond import LDMPipeline
     from .pipeline_utils import AudioPipelineOutput, DiffusionPipeline, ImagePipelineOutput
     from .pndm import PNDMPipeline
     from .repaint import RePaintPipeline
     from .score_sde_ve import ScoreSdeVePipeline
     from .stochastic_karras_ve import KarrasVePipeline

try:
     if not (is_torch_available() and is_librosa_available()):
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     from ..utils.dummy_torch_and_librosa_objects import *  # noqa F403
else:
     from .audio_diffusion import AudioDiffusionPipeline, Mel

try:
     if not (is_torch_available() and is_transformers_available()):
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     from ..utils.dummy_torch_and_transformers_objects import *  # noqa F403
else:
     from .alt_diffusion import AltDiffusionImgaImgPipeline, AltDiffusionPipeline
     from .audioldm import AudioLDMPipeline
     from .controlnet import (
         StableDiffusionControlNetImgaImgPipeline,
         StableDiffusionControlNetInpaintPipeline,
         StableDiffusionControlNetPipeline,
     )
     from .deepfloyd_if import (
         IFImgaImgPipeline,
         IFImgaImgSuperResolutionPipeline,
         IFInpaintingPipeline,
         IFInpaintingSuperResolutionPipeline,
         IFPipeline,
         IFSuperResolutionPipeline,
     )
     from .kandinsky import (
         KandinskyImgaImgPipeline,
         KandinskyInpaintPipeline,
         KandinskyPipeline,
         KandinskyPriorPipeline,
     )
     from .kandinskya_a import (
         KandinskyVaaControlnetImgaImgPipeline,
         KandinskyVaaControlnetPipeline,
         KandinskyVaaImgaImgPipeline,
         KandinskyVaaInpaintPipeline,
         KandinskyVaaPipeline,
         KandinskyVaaPriorEmbaEmbPipeline,
         KandinskyVaaPriorPipeline,
     )
     from .latent_diffusion import LDMTextToImagePipeline
     from .paint_by_example import PaintByExamplePipeline
     from .semantic_stable_diffusion import SemanticStableDiffusionPipeline
     from .shap_e import ShapEImgaImgPipeline, ShapEPipeline
     from .stable_diffusion import (
         CycleDiffusionPipeline,
         StableDiffusionAttendAndExcitePipeline,
         StableDiffusionDepthaImgPipeline,
         StableDiffusionDiffEditPipeline,
         StableDiffusionImageVariationPipeline,
         StableDiffusionImgaImgPipeline,
         StableDiffusionInpaintPipeline,
         StableDiffusionInpaintPipelineLegacy,
         StableDiffusionInstructPixaPixPipeline,
         StableDiffusionLatentUpscalePipeline,
         StableDiffusionLDMaDPipeline,
         StableDiffusionModelEditingPipeline,
         StableDiffusionPanoramaPipeline,
         StableDiffusionParadigmsPipeline,
         StableDiffusionPipeline,
         StableDiffusionPixaPixZeroPipeline,
         StableDiffusionSAGPipeline,
         StableDiffusionUpscalePipeline,
         StableUnCLIPImgaImgPipeline,
         StableUnCLIPPipeline,
     )
     from .stable_diffusion_safe import StableDiffusionPipelineSafe
     from .text_to_video_synthesis import TextToVideoSDPipeline, TextToVideoZeroPipeline, VideoToVideoSDPipeline
     from .unclip import UnCLIPImageVariationPipeline, UnCLIPPipeline
     from .unidiffuser import ImageTextPipelineOutput, UniDiffuserModel, UniDiffuserPipeline, UniDiffuserTextDecoder
     from .versatile_diffusion import (
         VersatileDiffusionDualGuidedPipeline,
         VersatileDiffusionImageVariationPipeline,
         VersatileDiffusionPipeline,
         VersatileDiffusionTextToImagePipeline,
     )
     from .vq_diffusion import VQDiffusionPipeline


try:
     if not (is_torch_available() and is_transformers_available() and is_invisible_watermark_available()):
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     from ..utils.dummy_torch_and_transformers_and_invisible_watermark_objects import *  # noqa F403
else:
     from .stable_diffusion_xl import StableDiffusionXLImgaImgPipeline, StableDiffusionXLPipeline

try:
     if not is_onnx_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     from ..utils.dummy_onnx_objects import *  # noqa F403
else:
     from .onnx_utils import OnnxRuntimeModel

try:
     if not (is_torch_available() and is_transformers_available() and is_onnx_available()):
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     from ..utils.dummy_torch_and_transformers_and_onnx_objects import *  # noqa F403
else:
     from .stable_diffusion import (
         OnnxStableDiffusionImgaImgPipeline,
         OnnxStableDiffusionInpaintPipeline,
         OnnxStableDiffusionInpaintPipelineLegacy,
         OnnxStableDiffusionPipeline,
         OnnxStableDiffusionUpscalePipeline,
         StableDiffusionOnnxPipeline,
     )

try:
     if not (is_torch_available() and is_transformers_available() and is_k_diffusion_available()):
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     from ..utils.dummy_torch_and_transformers_and_k_diffusion_objects import *  # noqa F403
else:
     from .stable_diffusion import StableDiffusionKDiffusionPipeline

try:
     if not is_flax_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     from ..utils.dummy_flax_objects import *  # noqa F403
else:
     from .pipeline_flax_utils import FlaxDiffusionPipeline


try:
     if not (is_flax_available() and is_transformers_available()):
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     from ..utils.dummy_flax_and_transformers_objects import *  # noqa F403
else:
     from .controlnet import FlaxStableDiffusionControlNetPipeline
     from .stable_diffusion import (
         FlaxStableDiffusionImgaImgPipeline,
         FlaxStableDiffusionInpaintPipeline,
         FlaxStableDiffusionPipeline,
     )
try:
     if not (is_transformers_available() and is_torch_available() and is_note_seq_available()):
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     from ..utils.dummy_transformers_and_torch_and_note_seq_objects import *  # noqa F403
else:
     from .spectrogram_diffusion import MidiProcessor, SpectrogramDiffusionPipeline
