from __future__ import annotations

UpperCAmelCase      		=					'''Alexander Joslin'''


def SCREAMING_SNAKE_CASE					(  lowercase_:						int					):

       if number <= 0:
              _UpperCamelCase  :							Union[str, Any]	    =	F"n must be greater than 0. Got n = {number}"
              raise ValueError(lowercase_					)

       _UpperCamelCase  :							List[str]	    =	[number + 1] * (number + 1)

       # starting position
       _UpperCamelCase  :							str	    =	0
       for i in range(1		,    lowercase_					):
              _UpperCamelCase  :							Optional[Any]	    =	min(table[i + 1]		,    table[i] + 1					)
              # check if out of bounds
              if i * 2 <= number:
                     _UpperCamelCase  :							Optional[Any]	    =	min(table[i * 2]		,    table[i] + 1					)
              # check if out of bounds
              if i * 3 <= number:
                     _UpperCamelCase  :							List[Any]	    =	min(table[i * 3]		,    table[i] + 1					)
       return table[number]


if __name__ == "__main__":
 import doctest

 doctest.testmod()










'''simple docstring'''






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



class  lowerCamelCase__				(						snake_case_						):


	"""simple docstring"""





	def __init__(					self   ,     *UpperCAmelCase__   ,     **UpperCAmelCase__			)       ->				Optional[int]:
					super().__init__(*UpperCAmelCase__   ,     **UpperCAmelCase__			)




	def 				_lowerCamelCase				(					self   ,     UpperCAmelCase__   ,     UpperCAmelCase__			)       ->				Optional[int]:
					_A :				Union[str, Any]				=  (
					    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 				_lowerCamelCase				(					self   ,     UpperCAmelCase__   ,     UpperCAmelCase__   ,     UpperCAmelCase__			)       ->				Union[str, Any]:
					return (increment * self.__hash_function_a(UpperCAmelCase__   ,     UpperCAmelCase__			)) % self.size_table




	def 				_lowerCamelCase				(					self   ,     UpperCAmelCase__   ,     UpperCAmelCase__=None			)       ->				List[Any]:
					_A :				Optional[int]				=  1
					_A :				Optional[int]				=  self.hash_function(UpperCAmelCase__			)

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

					return new_key
