code: 
  
  
  from itertools import permutations
  
  
  
  
  
  
  def 		_A		(		_lowercase = 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
       __UpperCamelCase   = list(range(gon_side + 1				,     0				,     -1   )   )
       __UpperCamelCase   = list(range(gon_side + 2				,     gon_side * 2 + 1   )   )
  
       for perm in permutations(small_numbers + big_numbers   ):
            __UpperCamelCase   = generate_gon_ring(_lowercase				,     list(_lowercase   )   )
            if is_magic_gon(_lowercase   ):
                 return int(''.join(str(_lowercase   ) for n in numbers   )   )
  
       __UpperCamelCase   = f'''Magic {gon_side}-gon ring is impossible'''
       raise ValueError(_lowercase   )
  
  
  
  
  
  
  def 		_A		(		_lowercase				,     _lowercase   )				->   list[int]:
  
  
       """simple docstring"""
  
  
       __UpperCamelCase   = [0] * (gon_side * 3)
       __UpperCamelCase   = perm[0:3]
       perm.append(perm[1]   )
  
       __UpperCamelCase   = 1 if gon_side < 5 else 2
  
       for i in range(1				,     len(_lowercase   ) // 3 + magic_number   ):
            __UpperCamelCase   = perm[2 * i + 1]
            __UpperCamelCase   = result[3 * i - 1]
            __UpperCamelCase   = perm[2 * i + 2]
  
       return result
  
  
  
  
  
  
  def 		_A		(		_lowercase   )				->   bool:
  
  
       """simple docstring"""
  
  
       if len(_lowercase   ) % 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   = sum(numbers[:3]   )
  
       return all(sum(numbers[i : i + 3]   ) == total for i in range(3				,     len(_lowercase   )				,     3   )   )
  
  
  if __name__ == "__main__":
      print(solution())
  
  
  
style_context: 
  
  
  from math import cos, sin
  
  
  
  
  
  
  def 		_A		(		_lowercase   )				->   list[list[float]]:
  
  
       """simple docstring"""
  
  
       __UpperCamelCase   = float(_lowercase   )
       return [[scaling_factor * int(x == y   ) for x in range(2   )] for y in range(2   )]
  
  
  
  
  
  
  def 		_A		(		_lowercase   )				->   list[list[float]]:
  
  
       """simple docstring"""
  
  
       __UpperCamelCase,						__UpperCamelCase   = cos(_lowercase   ), sin(_lowercase   )
       return [[c, -s], [s, c]]
  
  
  
  
  
  
  def 		_A		(		_lowercase   )				->   list[list[float]]:
  
  
       """simple docstring"""
  
  
       __UpperCamelCase,						__UpperCamelCase   = cos(_lowercase   ), sin(_lowercase   )
       __UpperCamelCase   = c * s
       return [[c * c, cs], [cs, s * s]]
  
  
  
  
  
  
  def 		_A		(		_lowercase   )				->   list[list[float]]:
  
  
       """simple docstring"""
  
  
       __UpperCamelCase,						__UpperCamelCase   = cos(_lowercase   ), sin(_lowercase   )
       __UpperCamelCase   = c * s
       return [[2 * c - 1, 2 * cs], [2 * cs, 2 * s - 1]]
  
  
  print(f"""    {scaling(5) = }""")
  print(f"""  {rotation(4_5) = }""")
  print(f"""{projection(4_5) = }""")
  
  
  print(f"""{reflection(4_5) = }""")
  
  
  