'''simple docstring'''




import math





def      _UpperCAmelCase    (							_UpperCamelCase    :	int   )	->      list[int]:
    if not isinstance(_UpperCamelCase,   _UpperCamelCase   ):
        A_     =   F'''Input value of [number={number}] must be an integer'''
        raise TypeError(_UpperCamelCase   )
    if number < 1:
        A_     =   F'''Input value of [number={number}] must be a positive integer'''
        raise ValueError(_UpperCamelCase   )
    A_     =   [number]
    while number != 1:
        if number % 2 == 0:
            A_     =   math.floor(math.sqrt(_UpperCamelCase   )   )
        else:
            A_     =   math.floor(
                math.sqrt(_UpperCamelCase   ) * math.sqrt(_UpperCamelCase   ) * math.sqrt(_UpperCamelCase   )   )
        sequence.append(_UpperCamelCase   )
    return sequence


if __name__ == "__main__":
  import doctest

  doctest.testmod()







'''simple docstring'''




import math





def      _UpperCAmelCase    (							_UpperCamelCase    :	int   )	->      float:
    A_     =   math.log(2,   10   ) * number
    A_     =   round((log_number - int(_UpperCamelCase   )),   15   )

    return difference





def      _UpperCAmelCase    (							_UpperCamelCase    :	int = 67_89_10   )	->      int:
    A_     =   90
    A_     =   0

    A_     =   math.log(1.2_3,   10   )
    A_     =   math.log(1.2_4,   10   )
    A_     =   0

    while position < number:
        A_     =   log_difference(_UpperCamelCase   )

        if difference >= upper_limit:
            power_iterator += 93

        elif difference < lower_limit:
            power_iterator += 1_96

        else:
            A_     =   power_iterator
            power_iterator += 1_96
            position += 1

    return previous_power


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  print(F"""{solution() = }""")






