code: 
  
  from __future__ import annotations
  
  A_:      int        =			"""Alexander Joslin"""
  
  
  def 					__lowerCAmelCase			(  _A					):
  
  
  
  							"""simple docstring"""
  
  
  							if number <= 0:
  														_lowercase				=	f'''n must be greater than 0. Got n = {number}'''
  														raise ValueError(_A					)
  
  							_lowercase				=	[number + 1] * (number + 1)
  
  							# starting position
  							_lowercase				=	0
  							for i in range(1 ,_A					):
  														_lowercase				=	min(table[i + 1] ,table[i] + 1					)
  														# check if out of bounds
  														if i * 2 <= number:
  																					_lowercase				=	min(table[i * 2] ,table[i] + 1					)
  														# check if out of bounds
  														if i * 3 <= number:
  																					_lowercase				=	min(table[i * 3] ,table[i] + 1					)
  							return table[number]
  
  
  if __name__ == "__main__":
  				import doctest
  
  				doctest.testmod()
  
  
  
style_context: def 					__lowerCAmelCase			(  _A = 998_001					):
  
  
  
  							"""simple docstring"""
  
  
  							_lowercase				=	0
  							for i in range(999 ,99 ,-1					):  # 3 digit numbers range from 999 down to 100
  														for j in range(999 ,99 ,-1					):
  																					_lowercase				=	str(i * j					)
  																					if product_string == product_string[::-1] and i * j < n:
  																												_lowercase				=	max(_A ,i * j					)
  							return answer
  
  
  if __name__ == "__main__":
  				print(F'''{solution() = }''')
  
  
  