




'''simple docstring'''





import math


def 					UpperCamelCase						(	snake_case ):




   '''simple docstring'''

   if not isinstance(snake_case						,  snake_case ):
      SCREAMING_SNAKE_CASE__      :					Dict							    =			f"""Input value of [number={number}] must be an integer"""
      raise TypeError(snake_case )
   if number < 1:
      SCREAMING_SNAKE_CASE__      :					List[Any]							    =			f"""Input value of [number={number}] must be a positive integer"""
      raise ValueError(snake_case )
   SCREAMING_SNAKE_CASE__      :					Tuple							    =			[number]
   while number != 1:
      if number % 2 == 0:
         SCREAMING_SNAKE_CASE__      :					Tuple							    =			math.floor(math.sqrt(snake_case ) )
      else:
         SCREAMING_SNAKE_CASE__      :					Any							    =			math.floor(
             math.sqrt(snake_case ) * math.sqrt(snake_case ) * math.sqrt(snake_case ) )
      sequence.append(snake_case )
   return sequence


if __name__ == "__main__":
       import doctest

       doctest.testmod()







'''simple docstring'''





import math
from decimal import Decimal, getcontext


def 					UpperCamelCase						(	snake_case = 4_00_00_00 ):




   '''simple docstring'''

   try:
      SCREAMING_SNAKE_CASE__      :					List[Any]							    =			int(snake_case )
   except (TypeError, ValueError):
      raise TypeError('''Parameter n must be int or castable to int.''' )
   if n <= 0:
      raise ValueError('''Parameter n must be greater than or equal to one.''' )
   SCREAMING_SNAKE_CASE__      :					Optional[int]							    =			1_00
   SCREAMING_SNAKE_CASE__      :					int							    =			(Decimal(5 ) ** Decimal(0.5 ) + 1) / Decimal(2 )

   SCREAMING_SNAKE_CASE__      :					int							    =			(math.floor(math.log(n * (phi + 2)						,  snake_case ) - 1 ) // 3) * 3 + 2
   SCREAMING_SNAKE_CASE__      :					int							    =			Decimal(round(phi ** Decimal(index + 1 ) ) ) / (phi + 2)
   SCREAMING_SNAKE_CASE__      :					Any							    =			num // 2
   return int(snake_case )


if __name__ == "__main__":
       print(F"{solution() = }")

