





from itertools import permutations
def 			__UpperCamelCase				(			lowercase__	:       Tuple = 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
    lowerCAmelCase_					:	str						=   list(range(gon_side + 1		,    0		,    -1		)		)
    lowerCAmelCase_					:	Dict						=   list(range(gon_side + 2		,    gon_side * 2 + 1		)		)

    for perm in permutations(small_numbers + big_numbers		):
        lowerCAmelCase_					:	Any						=   generate_gon_ring(__a		,    list(__a		)		)
        if is_magic_gon(__a		):
            return int("""""".join(str(__a		) for n in numbers		)		)

    lowerCAmelCase_					:	Optional[Any]						=   f'Magic {gon_side}-gon ring is impossible'
    raise ValueError(__a		)
def 			__UpperCamelCase				(			lowercase__	:       List[Any]		,    lowercase__	:       List[str]		)	->      list[int]:
    '''simple docstring'''





    lowerCAmelCase_					:	Union[str, Any]						=   [0] * (gon_side * 3)
    lowerCAmelCase_					:	str						=   perm[0:3]
    perm.append(perm[1]		)

    lowerCAmelCase_					:	List[str]						=   1 if gon_side < 5 else 2

    for i in range(1		,    len(__a		) // 3 + magic_number		):
        lowerCAmelCase_					:	Optional[int]						=   perm[2 * i + 1]
        lowerCAmelCase_					:	List[str]						=   result[3 * i - 1]
        lowerCAmelCase_					:	int						=   perm[2 * i + 2]

    return result
def 			__UpperCamelCase				(			lowercase__	:       List[Any]		)	->      bool:
    '''simple docstring'''





    if len(__a		) % 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_					:	Optional[int]						=   sum(numbers[:3]		)

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


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









from __future__ import annotations

import math
from itertools import permutations
def 			__UpperCamelCase				(			lowercase__	:       int		)	->      bool:
    '''simple docstring'''





    if 1 < number < 4:
        # 2 and 3 are primes
        return True
    elif number < 2 or number % 2 == 0 or number % 3 == 0:
        # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
        return False

    # All primes number are in format of 6k +/- 1
    for i in range(5		,    int(math.sqrt(lowercase__		) + 1		)		,    6		):
        if number % i == 0 or number % (i + 2) == 0:
            return False
    return True
def 			__UpperCamelCase				(			lowercase__	:       int = 7		)	->      int:
    '''simple docstring'''





    lowerCAmelCase_					:	str						=   """""".join(str(lowercase__		) for i in range(1		,    n + 1		)		)
    lowerCAmelCase_					:	Any						=   [int("""""".join(lowercase__		)		) for i in permutations(lowercase__		,    lowercase__		)]
    lowerCAmelCase_					:	List[Any]						=   [num for num in perm_list if is_prime(lowercase__		)]
    return max(lowercase__		) if pandigitals else 0


if __name__ == "__main__":
  print(f"""{solution() = }""")


