
'''simple docstring'''

from .hash_table import HashTable
from .number_theory.prime_numbers import is_prime, next_prime






class 				A       (		SCREAMING_SNAKE_CASE__      ):





	def __init__(   self     :    Optional[int] ,							*__magic_name__     :    Any ,							**__magic_name__     :    Optional[Any]							):


				"""simple docstring"""

				super().__init__(*__magic_name__ ,							**__magic_name__							)





	def 							__SCREAMING_SNAKE_CASE					(   self     :    Dict ,							__magic_name__     :    int ,							__magic_name__     :    Dict							):


				"""simple docstring"""

				lowerCAmelCase__									=							(
				    next_prime(value % self.size_table							)
				    if not is_prime(value % self.size_table							)
				    else value % self.size_table
				)  # gt = bigger than
				return next_prime_gt - (data % next_prime_gt)





	def 							__SCREAMING_SNAKE_CASE					(   self     :    Optional[Any] ,							__magic_name__     :    str ,							__magic_name__     :    Dict ,							__magic_name__     :    Dict							):


				"""simple docstring"""

				return (increment * self.__hash_function_a(__magic_name__ ,							__magic_name__							)) % self.size_table







	def 							__SCREAMING_SNAKE_CASE					(   self     :    Any ,							__magic_name__     :    Union[str, Any] ,							__magic_name__     :    Optional[int]=None							):


				"""simple docstring"""

				lowerCAmelCase__									=							1
				lowerCAmelCase__									=							self.hash_function(__magic_name__							)

				while self.values[new_key] is not None and self.values[new_key] != key:
							lowerCAmelCase__									=							(
							    self.__hash_double_function(__magic_name__ ,							__magic_name__ ,							__magic_name__							)
							    if self.balanced_factor() >= self.lim_charge
							    else None
							)
							if new_key is None:
										break
							else:
										i += 1

				return new_key







'''simple docstring'''

import math







def 					A       ( UpperCamelCase_   :       int )   ->    list:







			'''simple docstring'''



			if n <= 0:
						raise ValueError("Only positive integers have prime factors" )
			lowerCAmelCase__									=							[]
			while n % 2 == 0:
						pf.append(2 )
						lowerCAmelCase__									=							int(n / 2 )
			for i in range(3  ,		int(math.sqrt(UpperCamelCase_ ) ) + 1  ,		2 ):
						while n % i == 0:
									pf.append(UpperCamelCase_ )
									lowerCAmelCase__									=							int(n / i )
			if n > 2:
						pf.append(UpperCamelCase_ )
			return pf







def 					A       ( UpperCamelCase_   :       int )   ->    int:







			'''simple docstring'''



			if n <= 0:
						raise ValueError("Only positive numbers are accepted" )
			lowerCAmelCase__									=							1
			lowerCAmelCase__									=							1
			while n % 2 == 0:
						temp += 1
						lowerCAmelCase__									=							int(n / 2 )
			div *= temp
			for i in range(3  ,		int(math.sqrt(UpperCamelCase_ ) ) + 1  ,		2 ):
						lowerCAmelCase__									=							1
						while n % i == 0:
									temp += 1
									lowerCAmelCase__									=							int(n / i )
						div *= temp
			if n > 1:
						div *= 2
			return div







def 					A       ( UpperCamelCase_   :       int )   ->    int:







			'''simple docstring'''



			if n <= 0:
						raise ValueError("Only positive numbers are accepted" )
			lowerCAmelCase__									=							1
			lowerCAmelCase__									=							1
			while n % 2 == 0:
						temp += 1
						lowerCAmelCase__									=							int(n / 2 )
			if temp > 1:
						s *= (2**temp - 1) / (2 - 1)
			for i in range(3  ,		int(math.sqrt(UpperCamelCase_ ) ) + 1  ,		2 ):
						lowerCAmelCase__									=							1
						while n % i == 0:
									temp += 1
									lowerCAmelCase__									=							int(n / i )
						if temp > 1:
									s *= (i**temp - 1) / (i - 1)
			return int(UpperCamelCase_ )







def 					A       ( UpperCamelCase_   :       int )   ->    int:







			'''simple docstring'''



			lowerCAmelCase__									=							n
			for x in set(prime_factors(UpperCamelCase_ ) ):
						s *= (x - 1) / x
			return int(UpperCamelCase_ )


if __name__ == "__main__":
		import doctest

		doctest.testmod()





