code: 
  
  
  '''simple docstring'''
  
  from __future__ import annotations
  
  lowerCAmelCase   :Optional[Any]								=    '''Alexander Joslin'''
  
  
  
  
  
  def lowerCamelCase    (    lowerCAmelCase       :			int	):
  
  
  
  
  
  	"""simple docstring"""
  
  
  
  
  
  
  
  	if number <= 0:
  		__magic_name__ :					Any  			=  f'n must be greater than 0. Got n = {number}'
  		raise ValueError(lowerCAmelCase	)
  
  	__magic_name__ :					Optional[int]  			=  [number + 1] * (number + 1)
  
  	# starting position
  	__magic_name__ :					Optional[Any]  			=  0
  	for i in range(1	,	lowerCAmelCase	):
  		__magic_name__ :					List[str]  			=  min(table[i + 1]	,	table[i] + 1	)
  		# check if out of bounds
  		if i * 2 <= number:
  			__magic_name__ :					str  			=  min(table[i * 2]	,	table[i] + 1	)
  		# check if out of bounds
  		if i * 3 <= number:
  			__magic_name__ :					int  			=  min(table[i * 3]	,	table[i] + 1	)
  	return table[number]
  
  
  if __name__ == "__main__":
  							import doctest
  
  							doctest.testmod()
style_context: 
  
  
  '''simple docstring'''
  
  import math
  
  
  
  
  
  def lowerCamelCase    (    lowerCAmelCase       :			int	):
  
  
  
  
  
  	"""simple docstring"""
  
  
  
  
  
  
  
  	if not isinstance(lowerCAmelCase	,	lowerCAmelCase	):
  		__magic_name__ :					str  			=  f'Input value of [number={number}] must be an integer'
  		raise TypeError(lowerCAmelCase	)
  	if number < 1:
  		__magic_name__ :					Tuple  			=  f'Input value of [number={number}] must be a positive integer'
  		raise ValueError(lowerCAmelCase	)
  	__magic_name__ :					Tuple  			=  [number]
  	while number != 1:
  		if number % 2 == 0:
  			__magic_name__ :					Optional[int]  			=  math.floor(math.sqrt(lowerCAmelCase	)	)
  		else:
  			__magic_name__ :					Union[str, Any]  			=  math.floor(
  			    math.sqrt(lowerCAmelCase	) * math.sqrt(lowerCAmelCase	) * math.sqrt(lowerCAmelCase	)	)
  		sequence.append(lowerCAmelCase	)
  	return sequence
  
  
  if __name__ == "__main__":
  							import doctest
  
  							doctest.testmod()