code: 
  
  
  """simple docstring"""
  from __future__ import annotations
  
  from collections.abc import Iterable, Iterator
  from typing import Any, Generic, TypeVar
  
  UpperCAmelCase   =	TypeVar("""T""", bound=bool)
  
  
  
  
  class   lowercase__							(				Generic[T]							):
  
  
  
  
  
     def __init__(       self			,      SCREAMING_SNAKE_CASE)     ->     List[Any]:
        _lowerCamelCase  :				Optional[int]      =		value
        _lowerCamelCase  :				str      =		None
        _lowerCamelCase  :				Tuple      =		None
  
  
  
  
  
     @property
     def 		UpperCamelCase_     (       self)     ->     Dict:
        return self._value
  
  
  
  
  
     @staticmethod
     def 		UpperCamelCase_     (       SCREAMING_SNAKE_CASE			,      SCREAMING_SNAKE_CASE)     ->     List[Any]:
  
        if not roota:
           return roota
  
        if not roota:
           return roota
  
        if roota.value > roota.value:
           _lowerCamelCase      ,						_lowerCamelCase  :				List[str]      =		roota, roota
  
        _lowerCamelCase  :				Dict      =		roota
        _lowerCamelCase  :				Union[str, Any]      =		roota.right
        _lowerCamelCase  :				Optional[Any]      =		roota.left
        _lowerCamelCase  :				List[str]      =		SkewNode.merge(lowerCamelCase_			,      lowerCamelCase_)
  
        return result
  
  
  
  
  
  
  
  class   lowercase__							(				Generic[T]							):
  
  
  
  
  
     def __init__(       self			,      SCREAMING_SNAKE_CASE = ())     ->     Tuple:
        _lowerCamelCase  :				Union[str, Any]      =		None
        if data:
           for item in data:
              self.insert(lowerCamelCase_)
  
  
  
  
  
     def __bool__(       self)     ->     str:
        return self._root is not None
  
  
  
  
  
     def __iter__(       self)     ->     Optional[int]:
        _lowerCamelCase  :				List[str]      =		[]
        while self:
           result.append(self.pop())
  
        # Pushing items back to the heap not to clear it.
        for item in result:
           self.insert(lowerCamelCase_)
  
        return iter(lowerCamelCase_)
  
  
  
  
  
     def 		UpperCamelCase_     (       self			,      SCREAMING_SNAKE_CASE)     ->     Any:
        _lowerCamelCase  :				Any      =		SkewNode.merge(self._root			,      SkewNode(lowerCamelCase_))
  
  
  
  
  
     def 		UpperCamelCase_     (       self)     ->     List[Any]:
        _lowerCamelCase  :				Tuple      =		self.top()
        _lowerCamelCase  :				Dict      =		(
            SkewNode.merge(self._root.left			,      self._root.right) if self._root else None
        )
  
        return result
  
  
  
  
  
     def 		UpperCamelCase_     (       self)     ->     Dict:
  
        if not self._root:
           raise IndexError("""Can't get top element for the empty heap.""")
        return self._root.value
  
  
  
  
  
     def 		UpperCamelCase_     (       self)     ->     List[str]:
        _lowerCamelCase  :				Optional[int]      =		None
  
  
  if __name__ == "__main__":
   import doctest
  
   doctest.testmod()
  
  
  
  
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())
  
  