'''simple docstring'''


import math


def 					_lowerCamelCase    (      lowerCamelCase_					:							int   ):



     """simple docstring"""





     if not isinstance(_a	,     _a   ):
          UpperCAmelCase_							:   Optional[int]   =      F'''Input value of [number={number}] must be an integer'''
          raise TypeError(_a   )
     if number < 1:
          UpperCAmelCase_							:   Tuple   =      F'''Input value of [number={number}] must be a positive integer'''
          raise ValueError(_a   )
     UpperCAmelCase_							:   Tuple   =      [number]
     while number != 1:
          if number % 2 == 0:
               UpperCAmelCase_							:   Union[str, Any]   =      math.floor(math.sqrt(_a   )   )
          else:
               UpperCAmelCase_							:   Any   =      math.floor(
                   math.sqrt(_a   ) * math.sqrt(_a   ) * math.sqrt(_a   )   )
          sequence.append(_a   )
     return sequence


if __name__ == "__main__":
 import doctest

 doctest.testmod()














def    lowerCAmelCase__		(			_a				:	int			):
		if not isinstance(_a     ,					_a			):
				snake_case_ :							Optional[int]         =				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()
