




import math
from decimal import Decimal, getcontext

def   A   (   _SCREAMING_SNAKE_CASE = 400_0000					)			->				Union[str, Any]:







       try:
              lowerCamelCase     :   List[str]    				=      int(_A					)
       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."					)
       lowerCamelCase     :   Union[str, Any]    				=      100
       lowerCamelCase     :   List[Any]    				=      (Decimal(5					) ** Decimal(0.5					) + 1) / Decimal(2					)

       lowerCamelCase     :   Tuple    				=      (math.floor(math.log(n * (phi + 2)				,_A					) - 1					) // 3) * 3 + 2
       lowerCamelCase     :   List[Any]    				=      Decimal(round(phi ** Decimal(index + 1					)					)					) / (phi + 2)
       lowerCamelCase     :   int    				=      num // 2
       return int(_A					)


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








from __future__ import annotations

def   A   (   _SCREAMING_SNAKE_CASE				,_SCREAMING_SNAKE_CASE					)			->				list:
       lowerCamelCase     :   int    				=      [None] * (len(_SCREAMING_SNAKE_CASE					) + len(_SCREAMING_SNAKE_CASE					))

       lowerCamelCase     :   Any    				=      0  # pointer to current index for left Half
       lowerCamelCase     :   int    				=      0  # pointer to current index for the right Half
       lowerCamelCase     :   Optional[int]    				=      0  # pointer to current index for the sorted array Half

       while pointera < len(_SCREAMING_SNAKE_CASE					) and pointera < len(_SCREAMING_SNAKE_CASE					):
              if left_half[pointera] < right_half[pointera]:
                     lowerCamelCase     :   Any    				=      left_half[pointera]
                     pointera += 1
                     index += 1
              else:
                     lowerCamelCase     :   Any    				=      right_half[pointera]
                     pointera += 1
                     index += 1
       while pointera < len(_SCREAMING_SNAKE_CASE					):
              lowerCamelCase     :   Optional[Any]    				=      left_half[pointera]
              pointera += 1
              index += 1

       while pointera < len(_SCREAMING_SNAKE_CASE					):
              lowerCamelCase     :   str    				=      right_half[pointera]
              pointera += 1
              index += 1

       return sorted_array

def   A   (   _SCREAMING_SNAKE_CASE					)			->				list:
       if len(_SCREAMING_SNAKE_CASE					) <= 1:
              return array
       # the actual formula to calculate the middle element = left + (right - left) // 2
       # this avoids integer overflow in case of large N
       lowerCamelCase     :   int    				=      0 + (len(_SCREAMING_SNAKE_CASE					) - 0) // 2

       # Split the array into halves till the array length becomes equal to One
       # merge the arrays of single length returned by mergeSort function and
       # pass them into the merge arrays function which merges the array
       lowerCamelCase     :   Optional[Any]    				=      array[:middle]
       lowerCamelCase     :   Optional[Any]    				=      array[middle:]

       return merge(merge_sort(_SCREAMING_SNAKE_CASE					)				,merge_sort(_SCREAMING_SNAKE_CASE					)					)


if __name__ == "__main__":
       import doctest

       doctest.testmod()






