

from itertools import permutations




def        lowerCAmelCase(	SCREAMING_SNAKE_CASE_ = 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(__lowerCAmelCase       ,		list(__lowerCAmelCase       )       )
        if is_magic_gon(__lowerCAmelCase       ):
            return int("".join(str(__lowerCAmelCase       ) for n in numbers       )       )

    UpperCamelCase_          =		f"Magic {gon_side}-gon ring is impossible"
    raise ValueError(__lowerCAmelCase       )




def        lowerCAmelCase(	SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       )->		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(__lowerCAmelCase       ) // 3 + magic_number       ):
        UpperCamelCase_          =		perm[2 * i + 1]
        UpperCamelCase_          =		result[3 * i - 1]
        UpperCamelCase_          =		perm[2 * i + 2]

    return result




def        lowerCAmelCase(	SCREAMING_SNAKE_CASE_       )->		bool:



    """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

    UpperCamelCase_          =		sum(numbers[:3]       )

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


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

"""simple docstring"""


def 			lowerCamelCase_ (					__lowerCAmelCase				)							->					str:




						'''simple docstring'''



						lowerCamelCase__					=1
						lowerCamelCase__					=0
						lowerCamelCase__					=1
						lowerCamelCase__					=1
						lowerCamelCase__					=3
						lowerCamelCase__					=3
						lowerCamelCase__					=limit
						lowerCamelCase__					=0

						lowerCamelCase__					=""
						while counter != decimal + 1:
												if 4 * q + r - t < n * t:
																		result += str(__lowerCAmelCase				)
																		if counter == 0:
																								result += "."

																		if decimal == counter:
																								break

																		counter += 1
																		lowerCamelCase__					=10 * (r - n * t)
																		lowerCamelCase__					=((10 * (3 * q + r)) // t) - 10 * n
																		q *= 10
																		lowerCamelCase__					=nr
												else:
																		lowerCamelCase__					=(2 * q + r) * l
																		lowerCamelCase__					=(q * (7 * k) + 2 + (r * l)) // (t * l)
																		q *= k
																		t *= l
																		l += 2
																		k += 1
																		lowerCamelCase__					=nn
																		lowerCamelCase__					=nr
						return result





def 			lowerCamelCase_ (					)							->					None:




						'''simple docstring'''



						print(F'''{calculate_pi(50				) = }'''				)
						import doctest

						doctest.testmod()


if __name__ == "__main__":
	main()


