'''simple docstring'''

def __a			(						__lowerCamelCase      :    Dict					)						->				int:
      '''simple docstring'''


      if not isinstance(__a			,		__a					):
            lowercase_     			=   f'Input value of [number={number}] must be an integer'
            raise TypeError(__a					)
      if number < 1:
            raise ValueError("Input must be a positive integer"					)
      return number * (2 * number - 1)


if __name__ == "__main__":
       import doctest

       doctest.testmod()







'''simple docstring'''

from __future__ import annotations

_lowerCamelCase :				Optional[int]														= """Alexander Joslin"""



def  _lowerCAmelCase				(				__a      )  ->      int:
     '''simple docstring'''







     if number <= 0:
          _UpperCamelCase  :Optional[Any]       =F'''n must be greater than 0. Got n = {number}'''
          raise ValueError(__a      )

     _UpperCamelCase  :Optional[Any]       =[number + 1] * (number + 1)

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


if __name__ == "__main__":
      import doctest

      doctest.testmod()