code: 
  
  
  """simple docstring"""
  from typing import TYPE_CHECKING
  
  from ...utils import (
      OptionalDependencyNotAvailable,
      _LazyModule,
      is_tf_available,
      is_torch_available,
      is_vision_available,
  )
  
  
  UpperCAmelCase   =	{
      "configuration_sam": [
          "SAM_PRETRAINED_CONFIG_ARCHIVE_MAP",
          "SamConfig",
          "SamMaskDecoderConfig",
          "SamPromptEncoderConfig",
          "SamVisionConfig",
      ],
      "processing_sam": ["SamProcessor"],
  }
  
  
  try:
   if not is_torch_available():
    raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
   pass
  else:
   UpperCAmelCase   =	[
       "SAM_PRETRAINED_MODEL_ARCHIVE_LIST",
       "SamModel",
       "SamPreTrainedModel",
   ]
  try:
   if not is_tf_available():
    raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
   pass
  else:
   UpperCAmelCase   =	[
       "TF_SAM_PRETRAINED_MODEL_ARCHIVE_LIST",
       "TFSamModel",
       "TFSamPreTrainedModel",
   ]
  try:
   if not is_vision_available():
    raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
   pass
  else:
   UpperCAmelCase   =	["SamImageProcessor"]
  
  
  if TYPE_CHECKING:
   from .configuration_sam import (
       SAM_PRETRAINED_CONFIG_ARCHIVE_MAP,
       SamConfig,
       SamMaskDecoderConfig,
       SamPromptEncoderConfig,
       SamVisionConfig,
   )
   from .processing_sam import SamProcessor
  
   try:
    if not is_torch_available():
     raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
    pass
   else:
    from .modeling_sam import SAM_PRETRAINED_MODEL_ARCHIVE_LIST, SamModel, SamPreTrainedModel
  
   try:
    if not is_tf_available():
     raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
    pass
   else:
    from .modeling_tf_sam import TF_SAM_PRETRAINED_MODEL_ARCHIVE_LIST, TFSamModel, TFSamPreTrainedModel
  
   try:
    if not is_vision_available():
     raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
    pass
   else:
    from .image_processing_sam import SamImageProcessor
  
  else:
   import sys
  
   UpperCAmelCase   =	_LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)
  
  
  
  
style_context: 
  
  
  """simple docstring"""
  from itertools import permutations
  
  def 							_snake_case			(      __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
     _lowerCamelCase  :				Dict      =		list(range(gon_side + 1	,   0	,   -1      )      )
     _lowerCamelCase  :				Optional[int]      =		list(range(gon_side + 2	,   gon_side * 2 + 1      )      )
  
     for perm in permutations(small_numbers + big_numbers      ):
        _lowerCamelCase  :				List[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  :				Union[str, Any]      =		F'Magic {gon_side}-gon ring is impossible'
     raise ValueError(__snake_case      )
  
  def 							_snake_case			(      __snake_case       :			int	,   __snake_case       :			list[int]      ):
  
  
  
  
     """simple docstring"""
  
  
  
  
  
  
  
     _lowerCamelCase  :				Union[str, Any]      =		[0] * (gon_side * 3)
     _lowerCamelCase  :				Dict      =		perm[0:3]
     perm.append(perm[1]      )
  
     _lowerCamelCase  :				Tuple      =		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  :				str      =		result[3 * i - 1]
        _lowerCamelCase  :				Dict      =		perm[2 * i + 2]
  
     return result
  
  def 							_snake_case			(      __snake_case       :			list[int]      ):
  
  
  
  
     """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  :				str      =		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())
  
  