





"""simple docstring"""






from ..utils import DummyObject, requires_backends



class 						lowerCAmelCase       (   metaclass=snake_case				):
       lowerCAmelCase__    			=	["""torch""", """transformers""", """invisible_watermark"""]






       def __init__( self     ,	*a__     ,	**a__  ):
              requires_backends(self     ,	['torch', 'transformers', 'invisible_watermark']  )






       @classmethod
       def 				__A			( cls     ,	*a__     ,	**a__  ):
              requires_backends(cls     ,	['torch', 'transformers', 'invisible_watermark']  )






       @classmethod
       def 				__A			( cls     ,	*a__     ,	**a__  ):
              requires_backends(cls     ,	['torch', 'transformers', 'invisible_watermark']  )



class 						lowerCAmelCase       (   metaclass=snake_case				):
       lowerCAmelCase__    			=	["""torch""", """transformers""", """invisible_watermark"""]






       def __init__( self     ,	*a__     ,	**a__  ):
              requires_backends(self     ,	['torch', 'transformers', 'invisible_watermark']  )






       @classmethod
       def 				__A			( cls     ,	*a__     ,	**a__  ):
              requires_backends(cls     ,	['torch', 'transformers', 'invisible_watermark']  )






       @classmethod
       def 				__A			( cls     ,	*a__     ,	**a__  ):
              requires_backends(cls     ,	['torch', 'transformers', 'invisible_watermark']  )













"""simple docstring"""






from __future__ import annotations

def    __lowerCamelCase     (							SCREAMING_SNAKE_CASE,SCREAMING_SNAKE_CASE				)		->							list:






       """simple docstring"""




       _UpperCAmelCase			     =  [None] * (len(SCREAMING_SNAKE_CASE				) + len(SCREAMING_SNAKE_CASE				))

       _UpperCAmelCase			     =  0  # pointer to current index for left Half
       _UpperCAmelCase			     =  0  # pointer to current index for the right Half
       _UpperCAmelCase			     =  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]:
                     _UpperCAmelCase			     =  left_half[pointera]
                     pointera += 1
                     index += 1
              else:
                     _UpperCAmelCase			     =  right_half[pointera]
                     pointera += 1
                     index += 1
       while pointera < len(SCREAMING_SNAKE_CASE				):
              _UpperCAmelCase			     =  left_half[pointera]
              pointera += 1
              index += 1

       while pointera < len(SCREAMING_SNAKE_CASE				):
              _UpperCAmelCase			     =  right_half[pointera]
              pointera += 1
              index += 1

       return sorted_array

def    __lowerCamelCase     (							SCREAMING_SNAKE_CASE				)		->							list:






       """simple docstring"""




       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
       _UpperCAmelCase			     =  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
       _UpperCAmelCase			     =  array[:middle]
       _UpperCAmelCase			     =  array[middle:]

       return merge(merge_sort(SCREAMING_SNAKE_CASE				),merge_sort(SCREAMING_SNAKE_CASE				)				)


if __name__ == "__main__":
    import doctest

    doctest.testmod()






