


'''simple docstring'''






from maths.is_square_free import is_square_free
from maths.prime_factors import prime_factors







def 							UpperCamelCase_     (       A__   :  int   ):
  '''simple docstring'''





  lowerCAmelCase_     : Any     =  prime_factors(A__   )
  if is_square_free(A__   ):
    return -1 if len(A__   ) % 2 else 1
  return 0


if __name__ == "__main__":
  import doctest

  doctest.testmod()







'''simple docstring'''






from __future__ import annotations







def 							UpperCamelCase_     (       A__   :  list				,       A__   :  int				,       A__   :  int				,       A__   :  int   ):
  '''simple docstring'''





  lowerCAmelCase_     : int     =  []
  lowerCAmelCase_,				lowerCAmelCase_     : Any     =  input_list[low:mid], input_list[mid : high + 1]
  while left and right:
    result.append((left if left[0] <= right[0] else right).pop(0   )   )
  lowerCAmelCase_     : Dict     =  result + left + right
  return input_list







def 							UpperCamelCase_     (       A__   :  list   ):
  '''simple docstring'''





  if len(A__   ) <= 1:
    return input_list
  lowerCAmelCase_     : str     =  list(A__   )

  # iteration for two-way merging
  lowerCAmelCase_     : Dict     =  2
  while p <= len(A__   ):
    # getting low, high and middle value for merge-sort of single list
    for i in range(0				,       len(A__   )				,       A__   ):
      lowerCAmelCase_     : Tuple     =  i
      lowerCAmelCase_     : List[str]     =  i + p - 1
      lowerCAmelCase_     : Optional[Any]     =  (low + high + 1) // 2
      lowerCAmelCase_     : List[str]     =  merge(A__				,       A__				,       A__				,       A__   )
    # final merge of last two parts
    if p * 2 >= len(A__   ):
      lowerCAmelCase_     : Union[str, Any]     =  i
      lowerCAmelCase_     : Dict     =  merge(A__				,       0				,       A__				,       len(A__   ) - 1   )
      break
    p *= 2

  return input_list


if __name__ == "__main__":
  __A   :    int											= input("Enter numbers separated by a comma:\n").strip()
  if user_input == "":
    __A   :    str											= []
  else:
    __A   :    Optional[Any]											= [int(item.strip()) for item in user_input.split(",")]
  print(iter_merge_sort(unsorted))



