



'''simple docstring'''






import itertools




def        snake_case_   (	lowerCAmelCase_						)->						Dict:





       '''simple docstring'''


       return (
           int("""""".join(combination[0:2]						)						) * int("""""".join(combination[2:5]						)						)
           == int("""""".join(combination[5:9]						)						)
       ) or (
           int("""""".join(combination[0]						)						) * int("""""".join(combination[1:5]						)						)
           == int("""""".join(combination[5:9]						)						)
       )




def        snake_case_   (	)->						str:





       '''simple docstring'''


       return sum(
           {
               int("""""".join(pandigital[5:9]						)						)
               for pandigital in itertools.permutations("""123456789"""						)
               if is_combination_valid(lowerCAmelCase_						)
           }						)


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








"""simple docstring"""


from itertools import permutations

def 					_lowerCAmelCase (  lowercase_ = 5		):
						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 					_lowerCAmelCase (  lowercase_						,      lowercase_		):
						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 					_lowerCAmelCase (  lowercase_		):
						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())





