



'''simple docstring'''
from .number_theory.prime_numbers import next_prime



class _A  :





		def __init__(     self ,       __UpperCAmelCase ,       __UpperCAmelCase = None ,       __UpperCAmelCase = None ,       )       ->     None:

					'''simple docstring'''
					__UpperCAmelCase   :      List[str]										=     size_table
					__UpperCAmelCase   :      str										=     [None] * self.size_table
					__UpperCAmelCase   :      Optional[Any]										=     0.75 if lim_charge is None else lim_charge
					__UpperCAmelCase   :      Tuple										=     1 if charge_factor is None else charge_factor
					__UpperCAmelCase   :      list										=     []
					__UpperCAmelCase   :      dict										=     {}





		def 							__A       (     self				)       ->     Any:

					'''simple docstring'''
					return self._keys





		def 							__A       (     self				)       ->     List[str]:

					'''simple docstring'''
					return sum(1 for slot in self.values if slot is not None				) / (
					    self.size_table * self.charge_factor
					)





		def 							__A       (     self ,       __UpperCAmelCase				)       ->     Any:

					'''simple docstring'''
					return key % self.size_table





		def 							__A       (     self ,       __UpperCAmelCase				)       ->     str:

					'''simple docstring'''
					print(f'step {step_ord}'				)
					print(list(range(len(self.values				)				)				)				)
					print(self.values				)





		def 							__A       (     self ,       __UpperCAmelCase				)       ->     Dict:

					'''simple docstring'''
					__UpperCAmelCase   :      Union[str, Any]										=     1
					__UpperCAmelCase   :      Any										=     values
					for value in values:
								self.insert_data(__UpperCAmelCase				)
								self._step_by_step(__UpperCAmelCase				)
								i += 1





		def 							__A       (     self ,       __UpperCAmelCase ,       __UpperCAmelCase				)       ->     Optional[int]:

					'''simple docstring'''
					__UpperCAmelCase   :      Optional[int]										=     data
					__UpperCAmelCase   :      Tuple										=     data





		def 							__A       (     self ,       __UpperCAmelCase ,       __UpperCAmelCase=None				)       ->     Dict:

					'''simple docstring'''
					__UpperCAmelCase   :      List[str]										=     self.hash_function(key + 1				)

					while self.values[new_key] is not None and self.values[new_key] != key:
								if self.values.count(__UpperCAmelCase				) > 0:
											__UpperCAmelCase   :      Optional[Any]										=     self.hash_function(new_key + 1				)
								else:
											__UpperCAmelCase   :      Optional[int]										=     None
											break

					return new_key





		def 							__A       (     self				)       ->     List[Any]:

					'''simple docstring'''
					__UpperCAmelCase   :      int										=     [value for value in self.values if value is not None]
					__UpperCAmelCase   :      Union[str, Any]										=     next_prime(self.size_table ,       factor=2				)
					self._keys.clear()
					__UpperCAmelCase   :      List[str]										=     [None] * self.size_table  # hell's pointers D: don't DRY ;/
					for value in survivor_values:
								self.insert_data(__UpperCAmelCase				)





		def 							__A       (     self ,       __UpperCAmelCase				)       ->     List[str]:

					'''simple docstring'''
					__UpperCAmelCase   :      Dict										=     self.hash_function(__UpperCAmelCase				)

					if self.values[key] is None:
								self._set_value(__UpperCAmelCase ,       __UpperCAmelCase				)

					elif self.values[key] == data:
								pass

					else:
								__UpperCAmelCase   :      Union[str, Any]										=     self._collision_resolution(__UpperCAmelCase ,       __UpperCAmelCase				)
								if collision_resolution is not None:
											self._set_value(__UpperCAmelCase ,       __UpperCAmelCase				)
								else:
											self.rehashing()
											self.insert_data(__UpperCAmelCase				)









'''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())




