


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())






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) = }""")


