



'''simple docstring'''
import math


def   lowercase_	(   lowerCAmelCase__	:  int ):

			"""simple docstring"""





			__UpperCAmelCase   :      List[str]										=     math.log(2			,							10 ) * number
			__UpperCAmelCase   :      Dict										=     round((log_number - int(lowerCAmelCase__ ))			,							15 )

			return difference


def   lowercase_	(   lowerCAmelCase__	:  int = 678910 ):

			"""simple docstring"""





			__UpperCAmelCase   :      Any										=     90
			__UpperCAmelCase   :      Any										=     0

			__UpperCAmelCase   :      Union[str, Any]										=     math.log(1.23			,							10 )
			__UpperCAmelCase   :      str										=     math.log(1.24			,							10 )
			__UpperCAmelCase   :      Union[str, Any]										=     0

			while position < number:
						__UpperCAmelCase   :      List[str]										=     log_difference(lowerCAmelCase__ )

						if difference >= upper_limit:
									power_iterator += 93

						elif difference < lower_limit:
									power_iterator += 196

						else:
									__UpperCAmelCase   :      str										=     power_iterator
									power_iterator += 196
									position += 1

			return previous_power


if __name__ == "__main__":
					import doctest

					doctest.testmod()

					print(F'{solution() = }')









'''simple docstring'''
from itertools import permutations


def   lowercase_	(   lowerCAmelCase__	:  int = 5 ):

			"""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   :      int										=     list(range(gon_side + 1			,							0			,							-1 ) )
			__UpperCAmelCase   :      int										=     list(range(gon_side + 2			,							gon_side * 2 + 1 ) )

			for perm in permutations(small_numbers + big_numbers ):
						__UpperCAmelCase   :      Optional[int]										=     generate_gon_ring(lowerCAmelCase__			,							list(lowerCAmelCase__ ) )
						if is_magic_gon(lowerCAmelCase__ ):
									return int("""""".join(str(lowerCAmelCase__ ) for n in numbers ) )

			__UpperCAmelCase   :      Optional[int]										=     f'Magic {gon_side}-gon ring is impossible'
			raise ValueError(lowerCAmelCase__ )


def   lowercase_	(   lowerCAmelCase__	:  int			,							lowerCAmelCase__	:  list[int] ):

			"""simple docstring"""





			__UpperCAmelCase   :      Tuple										=     [0] * (gon_side * 3)
			__UpperCAmelCase   :      Optional[Any]										=     perm[0:3]
			perm.append(perm[1] )

			__UpperCAmelCase   :      Union[str, Any]										=     1 if gon_side < 5 else 2

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

			return result


def   lowercase_	(   lowerCAmelCase__	:  list[int] ):

			"""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   :      Optional[int]										=     sum(numbers[:3] )

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


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




